A few more things to add...
I posted in another thread about the 1989-91 Batman comic strip by Max Allan Collins and Marshall Rogers, and how the series was commissioned as a kind of follow-up to the 1989 movie. In that regard, the comic strip itself can be seen as an alternative sequel to the movie. Especially since the first two villains to appear in it were Catwoman and the Penguin. In the Catwoman storyline, the depiction of Selina Kyle is quite different from the version in the mainstream comics at the time.
Unlike the pre-Zero Hour comics, this version of Catwoman is a cold-blooded killer. She slashes people to death with her claws and displays no remorse afterwards. This has to be one of the most vicious interpretations of the character I've seen in any medium.
It should be instantly familiar to anyone who's read Sam Hamm's script for Batman 2. The early plot point in Hamm's script about Batman being blamed for a recent spate of vigilante killings – when in reality it is Catwoman who is responsible – was taken directly from this comic. The overall characterisation of Catwoman as a cold-blooded killer is also consistent with Hamm's script.

The Catwoman in Batman: The Animated Series was also influenced by this comic strip. Perhaps most notably in Catwoman's alter ego. Here Selina is depicted as a wealthy philanthropist who runs an art gallery in order to raise money to help disadvantaged youths. The comic story ends with Batman and Catwoman about to embrace, only for Batman to suddenly slap a pair of handcuffs on her. This was reused in 'The Cat and the Claw' two-parter in the TV show.

As far as her origin story goes, this Selina was a member of a gang of drug dealers known as the Crime Alley Cats. Selina was the girlfriend of the gang's leader and sold drugs on his behalf, which in turn resulted in her being arrested and sent to prison.

Selina then kicked the habit and decided to turn her life around. She started by targeting the very gang she'd once served. The first few times we see her she's attacking drug dealers in alleyways. Sometimes she kills them, other times she simply slashes their faces with her claws and sends them off to warn the other drug dealers. These scenes are visually similar to Catwoman's first costumed scene in Catwoman: Her Sister's Keeper where she slashes Stan's face after fighting him in an alley; or her first costumed scene in Batman Returns where she slashes the face of a would-be rapist.

Batman intercedes and stops her from killing a drug dealer. She says that she became Catwoman following his example, and he tells her it's not their place to kill lowlifes. The underlying theme behind their conversation is similar to their discussions about Shreck in Batman Returns.

It turns out that all the drugs are coming from a rich gangster named Mr. 'Bull' Pitt. He could be seen as the Max Shreck of this story, and it's ultimately him that Selina goes after. She finally kills him by pulling him out of the window of his office - an inversion of what Shreck did to Selina in the movie.

This story also features a nine-lives gag.

Here are some more comics dealing with the nine-lives motif.
I mentioned a while ago that two Catwoman comic stories were referenced in the comic history chapter of Michael Singer's Batman Returns: The Official Movie Book – 'Shadow of the Cat' (Batman #323 – 324, 1980) and Catwoman: Her Sister's Keeper. I've already written quite a bit about Catwoman: Her Sister's Keeper, which was of course the canonical origin story of the pre-Zero Hour Catwoman before it was retconned in 1993. But after rereading 'Shadow of the Cat' I've found some more things to say about that story too.
First of all, the cover art.

There's a certain Batman Returns vibe going on here. Both covers show Batman and Catwoman in the sewers. On the first cover we see Catwoman attacking Batman with her claws. A classic snapshot of the Batman/Catwoman feud, except here Batman isn't striking back. That's because this story took place during the period when Selina had reformed and was living a law-abiding life. She reassumes the mantle in this story because she was told in the previous issue – 'Chaos – Coming and Going!' (Batman #322, 1980) – that she had contracted an exotic disease during her tenure as Catwoman, and that if she didn't steal a rare Egyptian remedy she'd be dead within a month. In this story Cat-Man has stolen the remedy from a museum and Catwoman has been blamed. So she sets off to recover the medicine and get revenge on Cat-Man. Batman's role is to try and resolve the situation while steering Selina back onto the path of lawfulness, similar to the finale of Batman Returns. The second cover shows what might have been had Batman found Selina's remains at the end of the movie – emerging from the sewers in his own damaged costume, carrying the wounded Selina in his arms.
What's most interesting about this story though is that it marks the end of the 'nine lives' story arc that began with the introduction of Cat-Man back in the 1960s. To properly explain this we need to look at the history of the Cat-Man character, as well as Bob Kane's original concept behind the Cat-villain motif. On page 16 of Batman Returns: The Official Movie Book the question of why Selina dresses as a cat is directed at Kane.
This element of feline endurance was the earliest characteristic to be displayed by the character in the comics, even before she got her cowl, claws, whip or alter ego. Back when she was simply known as 'The Cat' she still displayed this uncanny ability to pull off unlikely escapes. At the end of her first appearance in 'The Cat' (Batman #1, 1940) she leaps out of a speeding motorboat into the sea. At the end of her second appearance in 'The Joker Meets the Cat-Woman' (Detective Comics #2, 1940) she jumps from a rope ladder hanging from the Bat-Plane and plummets into the sea again. Both times escaping from Batman and evading capture.
This survival-trait of the character, along with her flirty relationship with Batman, were the earliest recurring elements of Catwoman's personality. I've already mentioned some other stories that highlighted the nine-lives theme in more detail – specifically the Golden Age story 'Nine Lives Has the Catwoman' and the Silver Age story 'The Case of the Purr-loined Pearl!'. But the comic writers went on to explore it in more detail through the character of Cat-Man.
Cat-Man first appeared in 'The Challenge of the Cat-Man' (Detective Comics #311, January 1963). At the end of that story he appeared to perish after plunging over a cataract. Batman wonders if there's any truth to the notion that cats have nine lives...

...and clearly there is, for Cat-Man returned later that year in 'The Cat-Man Strikes Back' (Detective Comics #318, August 1963). At the end of this story he seemingly dies again, this time when he crashes his motorboat into a buoy and it explodes. Batman again wonders if he could have survived since he still has seven lives left.

And of course Cat-Man returned yet again in 'The Strange Lives of the Cat-Man' (Detective Comics #325, March 1964). Here it was explained that Cat-Man's nine lives were indeed supernatural. Apparently he'd made his costume from a material from a Pacific island where the natives worshipped cats. In later comics the supernatural properties of his costume would be treated with more ambiguity, suggesting that his survival stemmed from good luck rather than paranormal causes. But in this story it is clearly, unambiguously supernatural. Cat-Man loses his third life when he dives off a cliff....

...his fourth life when he gets electrocuted...

...and his fifth life when he walks through fire.

Batwoman then dresses in the Cat-Woman costume Cat-Man made for her using the materials from his own suit. She uses up three of his four remaining lives – once to save Batman and Robin from the burning rooftop where Cat-Man had left them, a second time after driving her motorcycle over a ravine, and a third time when she leaps from a skyscraper. With only one life remaining, Cat-Man is then safely locked away behind bars.

Cat-Man didn't face off against Batman again for another 16 years, but he did finally return in the Bronze Age story 'Shadow of the Cat'. As mentioned earlier, Selina Kyle was dying from a recently diagnosed illness. At the end of the story she makes a miraculous recovery from this disease after ripping off part of Cat-Man's costume. The ending is ambiguous, with Bruce Wayne doubting the supernatural nature of her recovery but at a loss to explain it in any other way. Selina herself firmly believes that she has survived by taking one of Cat-Man's nine lives for herself.

Unlike previous stories – where Catwoman's nine-lives ability was presented as simply good luck or trickery – it is here presented as 100% supernatural. This event would be mentioned in later comics whenever Catwoman and Cat-Man clashed; with both of them believing that Selina stole one of Blake's lives, even though the other characters remain sceptical. And as I mentioned earlier, 'Shadow of the Cat' was referenced in the Batman Returns movie book. Coincidence? Perhaps...
Most comics don't bother to explain or justify why Selina dresses as a cat. Batman Returns is one of the few times a compelling reason was given to explain why she did. In creating ambiguity regarding her nine lives, Burton restored the mystical totemic dimension to the character that'd been absent from the comics since the pre-Crisis era. In short, by having Selina relate her good luck to her feline totem, it created a valid psychological reason for her to adopt the mantle of the cat. It doesn't matter if she really does possess supernatural abilities (and according to Burton's DVD commentary she doesn't); it only matters that she believes she does and that she relates her own survival instincts to her totem. I would argue that this is best explanation to date for why she would dress as a cat. If you approach the issue from a rational standpoint it makes no sense why a female criminal would dress as a cat instead of simply wearing a less conspicuous stealth suit. But if you approach it from a psychological/mystical perspective like Burton did, it starts to make more sense. At least that's what I think.
Anyway, that's all I've got on Batman Returns for the moment.
I posted in another thread about the 1989-91 Batman comic strip by Max Allan Collins and Marshall Rogers, and how the series was commissioned as a kind of follow-up to the 1989 movie. In that regard, the comic strip itself can be seen as an alternative sequel to the movie. Especially since the first two villains to appear in it were Catwoman and the Penguin. In the Catwoman storyline, the depiction of Selina Kyle is quite different from the version in the mainstream comics at the time.
Unlike the pre-Zero Hour comics, this version of Catwoman is a cold-blooded killer. She slashes people to death with her claws and displays no remorse afterwards. This has to be one of the most vicious interpretations of the character I've seen in any medium.
It should be instantly familiar to anyone who's read Sam Hamm's script for Batman 2. The early plot point in Hamm's script about Batman being blamed for a recent spate of vigilante killings – when in reality it is Catwoman who is responsible – was taken directly from this comic. The overall characterisation of Catwoman as a cold-blooded killer is also consistent with Hamm's script.

The Catwoman in Batman: The Animated Series was also influenced by this comic strip. Perhaps most notably in Catwoman's alter ego. Here Selina is depicted as a wealthy philanthropist who runs an art gallery in order to raise money to help disadvantaged youths. The comic story ends with Batman and Catwoman about to embrace, only for Batman to suddenly slap a pair of handcuffs on her. This was reused in 'The Cat and the Claw' two-parter in the TV show.

As far as her origin story goes, this Selina was a member of a gang of drug dealers known as the Crime Alley Cats. Selina was the girlfriend of the gang's leader and sold drugs on his behalf, which in turn resulted in her being arrested and sent to prison.

Selina then kicked the habit and decided to turn her life around. She started by targeting the very gang she'd once served. The first few times we see her she's attacking drug dealers in alleyways. Sometimes she kills them, other times she simply slashes their faces with her claws and sends them off to warn the other drug dealers. These scenes are visually similar to Catwoman's first costumed scene in Catwoman: Her Sister's Keeper where she slashes Stan's face after fighting him in an alley; or her first costumed scene in Batman Returns where she slashes the face of a would-be rapist.

Batman intercedes and stops her from killing a drug dealer. She says that she became Catwoman following his example, and he tells her it's not their place to kill lowlifes. The underlying theme behind their conversation is similar to their discussions about Shreck in Batman Returns.

It turns out that all the drugs are coming from a rich gangster named Mr. 'Bull' Pitt. He could be seen as the Max Shreck of this story, and it's ultimately him that Selina goes after. She finally kills him by pulling him out of the window of his office - an inversion of what Shreck did to Selina in the movie.

This story also features a nine-lives gag.

Here are some more comics dealing with the nine-lives motif.
I mentioned a while ago that two Catwoman comic stories were referenced in the comic history chapter of Michael Singer's Batman Returns: The Official Movie Book – 'Shadow of the Cat' (Batman #323 – 324, 1980) and Catwoman: Her Sister's Keeper. I've already written quite a bit about Catwoman: Her Sister's Keeper, which was of course the canonical origin story of the pre-Zero Hour Catwoman before it was retconned in 1993. But after rereading 'Shadow of the Cat' I've found some more things to say about that story too.
First of all, the cover art.

There's a certain Batman Returns vibe going on here. Both covers show Batman and Catwoman in the sewers. On the first cover we see Catwoman attacking Batman with her claws. A classic snapshot of the Batman/Catwoman feud, except here Batman isn't striking back. That's because this story took place during the period when Selina had reformed and was living a law-abiding life. She reassumes the mantle in this story because she was told in the previous issue – 'Chaos – Coming and Going!' (Batman #322, 1980) – that she had contracted an exotic disease during her tenure as Catwoman, and that if she didn't steal a rare Egyptian remedy she'd be dead within a month. In this story Cat-Man has stolen the remedy from a museum and Catwoman has been blamed. So she sets off to recover the medicine and get revenge on Cat-Man. Batman's role is to try and resolve the situation while steering Selina back onto the path of lawfulness, similar to the finale of Batman Returns. The second cover shows what might have been had Batman found Selina's remains at the end of the movie – emerging from the sewers in his own damaged costume, carrying the wounded Selina in his arms.
What's most interesting about this story though is that it marks the end of the 'nine lives' story arc that began with the introduction of Cat-Man back in the 1960s. To properly explain this we need to look at the history of the Cat-Man character, as well as Bob Kane's original concept behind the Cat-villain motif. On page 16 of Batman Returns: The Official Movie Book the question of why Selina dresses as a cat is directed at Kane.
QuoteWhy a cat? "Well, a cat has nine lives," Kane emphasizes. "So I figured that whenever she was caught, or wounded, she would survive and live again for another go-round with Batman."
This element of feline endurance was the earliest characteristic to be displayed by the character in the comics, even before she got her cowl, claws, whip or alter ego. Back when she was simply known as 'The Cat' she still displayed this uncanny ability to pull off unlikely escapes. At the end of her first appearance in 'The Cat' (Batman #1, 1940) she leaps out of a speeding motorboat into the sea. At the end of her second appearance in 'The Joker Meets the Cat-Woman' (Detective Comics #2, 1940) she jumps from a rope ladder hanging from the Bat-Plane and plummets into the sea again. Both times escaping from Batman and evading capture.
This survival-trait of the character, along with her flirty relationship with Batman, were the earliest recurring elements of Catwoman's personality. I've already mentioned some other stories that highlighted the nine-lives theme in more detail – specifically the Golden Age story 'Nine Lives Has the Catwoman' and the Silver Age story 'The Case of the Purr-loined Pearl!'. But the comic writers went on to explore it in more detail through the character of Cat-Man.
Cat-Man first appeared in 'The Challenge of the Cat-Man' (Detective Comics #311, January 1963). At the end of that story he appeared to perish after plunging over a cataract. Batman wonders if there's any truth to the notion that cats have nine lives...

...and clearly there is, for Cat-Man returned later that year in 'The Cat-Man Strikes Back' (Detective Comics #318, August 1963). At the end of this story he seemingly dies again, this time when he crashes his motorboat into a buoy and it explodes. Batman again wonders if he could have survived since he still has seven lives left.

And of course Cat-Man returned yet again in 'The Strange Lives of the Cat-Man' (Detective Comics #325, March 1964). Here it was explained that Cat-Man's nine lives were indeed supernatural. Apparently he'd made his costume from a material from a Pacific island where the natives worshipped cats. In later comics the supernatural properties of his costume would be treated with more ambiguity, suggesting that his survival stemmed from good luck rather than paranormal causes. But in this story it is clearly, unambiguously supernatural. Cat-Man loses his third life when he dives off a cliff....

...his fourth life when he gets electrocuted...

...and his fifth life when he walks through fire.

Batwoman then dresses in the Cat-Woman costume Cat-Man made for her using the materials from his own suit. She uses up three of his four remaining lives – once to save Batman and Robin from the burning rooftop where Cat-Man had left them, a second time after driving her motorcycle over a ravine, and a third time when she leaps from a skyscraper. With only one life remaining, Cat-Man is then safely locked away behind bars.

Cat-Man didn't face off against Batman again for another 16 years, but he did finally return in the Bronze Age story 'Shadow of the Cat'. As mentioned earlier, Selina Kyle was dying from a recently diagnosed illness. At the end of the story she makes a miraculous recovery from this disease after ripping off part of Cat-Man's costume. The ending is ambiguous, with Bruce Wayne doubting the supernatural nature of her recovery but at a loss to explain it in any other way. Selina herself firmly believes that she has survived by taking one of Cat-Man's nine lives for herself.

Unlike previous stories – where Catwoman's nine-lives ability was presented as simply good luck or trickery – it is here presented as 100% supernatural. This event would be mentioned in later comics whenever Catwoman and Cat-Man clashed; with both of them believing that Selina stole one of Blake's lives, even though the other characters remain sceptical. And as I mentioned earlier, 'Shadow of the Cat' was referenced in the Batman Returns movie book. Coincidence? Perhaps...
Most comics don't bother to explain or justify why Selina dresses as a cat. Batman Returns is one of the few times a compelling reason was given to explain why she did. In creating ambiguity regarding her nine lives, Burton restored the mystical totemic dimension to the character that'd been absent from the comics since the pre-Crisis era. In short, by having Selina relate her good luck to her feline totem, it created a valid psychological reason for her to adopt the mantle of the cat. It doesn't matter if she really does possess supernatural abilities (and according to Burton's DVD commentary she doesn't); it only matters that she believes she does and that she relates her own survival instincts to her totem. I would argue that this is best explanation to date for why she would dress as a cat. If you approach the issue from a rational standpoint it makes no sense why a female criminal would dress as a cat instead of simply wearing a less conspicuous stealth suit. But if you approach it from a psychological/mystical perspective like Burton did, it starts to make more sense. At least that's what I think.
Anyway, that's all I've got on Batman Returns for the moment.