To elaborate on that a little, having characters escape from Arkham Asylum is a constant in the Batman universe.

At least two episodes in Batman: The Dark Knight Returns involved characters being released from Arkham (Two Face and The Joker). A big part of the ending of Batman Begins was when Arkham asylum was opened up.

Plots like that aren't even confined to DC. I was just looking through a Nintendo Power that reviewed Maximum Carnage (and, incidentally, also reviewed Final Fantasy III for SNES), and Carnage escapes from an asylum at the beginning of that game.