Catwoman (Arkhamverse)

Batman: Arkham Asylum
While Catwoman does not appear in the video game Batman: Arkham Asylum, her clawed gloves and mask appear on display at the East Wing Corridor of the old Arkham Mansion, suggesting she was, or is an inmate.

Batman: Arkham City
Catwoman was revealed to be appearing and playable in Batman: Arkham City, voiced by Grey DeLisle. She appears on two different covers for the magazine Gameinformer along with Batman possibly suggesting Catwoman will have a large role in the game. After Arkham Asylum's former administrator, Quincy Sharp, wins the election to become mayor of Gotham, he imprisons all prisoners and mental patients from local Blackgate Prison and Arkham Asylum within a sealed-off perimeter known as 'Arkham City', including Catwoman. Lawlessness reigns and armed mercenaries patrol the walls of the prison city to ensure no one attempts to escape, with Sharp hoping that the society of villains housed inside will kill each other and rid Gotham of its worst criminals. While in Arkham City, she infiltrated the former Arkham Asylum to steal a memory flashdrive that was being kept in a safe (presumably the same one that killed Penelope Young), beating up members of Two-Face's gang (who initially mistook her for Batman), but ended up captured by Two-Face by gunpoint after breaking into the safe and stealing it. She was then about to be publically executed by Two-Face in the courthouse, both due to her previous theft and as a means to ensure Two Face would rise in the ranks of Arkham City. Two-Face then decided after flipping a coin to hold a trial instead of killing her immediately. This ultimately gave Batman enough time to infiltrate the courtroom and beat up his gang. After she is saved by Batman, she doesn't elaborate on any knowledge on what is going on in Arkham City or on what Hugo Strange is up to, but she doesn't trust the latter either way as he was absent for a year and then came under command of Sharp. She also narrowly evades a sniper shot from the Joker.

Arkham City Profile: Dr. Hugo Strange
Selina Kyle A.K.A Catwoman

Her agility and razor-sharp claws will buy Catwoman some time in Arkham City, but without a strong ally or power base it is unlikely that she will remain unscratched for long. Catwoman's best chance is to team up with one or more of the other villains, who are able to offer her some protection in return for her special skills -- she is perhaps one of the greatest thieves in the world.

Dr. Hugo Strange: Side Note

Working alone, Catwoman’s chances of survival in her new high-security home are slim.

~ Dr. Hugo Strange