Well, there are plenty of excuses, but only psychological. There's no doubt in my mind that he was wrong to do so. She was even less right to shoot him, though.
Maybe it's not supposed to, but Gotham Central is the closest thing Gotham has to the real world, so it does matter.
I agree entirely that cops have a right to their grudge against Batman, but having a grudge against someone doesn't justify shooting them.