Eh, not really. Is a police officer who decides not to kill a criminal who eventually gets out of prison and commits more murder responsible for those deaths? It's similar to the trolley problem.

The general form of the problem is this: There is a runaway trolley barreling down the railway tracks. Ahead, on the tracks, there are five people tied up and unable to move. The trolley is headed straight for them. You are standing some distance off in the train yard, next to a lever. If you pull this lever, the trolley will switch to a different set of tracks. However, you notice that there is one person on the side track. You have two options:

(1) Do nothing, and the trolley kills the five people on the main track.

(2) Pull the lever, diverting the trolley onto the side track where it will kill one person. Which is the correct choice?

You could make very convincing arguments for either position, but at the end of the day, not pulling the lever doesn't make you at all responsible for the deaths of the five people in option 1, even though you could have prevented them. Being able to prevent an act from occurring but not doing so doesn't automatically make you responsible for that act. That would be an extremely slippery slope.

Batman shouldn't be the one to kill people. There's this magical thing called the justice system that has been used for thousands of years to deal with these cases. Crime fighting isn't Batman's job; he does it because he wants to. He hands Joker over every single time and the justice system is too stupid to put him in the chair. That's their job. If Batman kills Joker he becomes a murderer himself.