In this case, I thought we were talking about killing the Joker. We hadn't spoken of the conditions, but I'd understood you meant 'killing the Joker' as an absolute, without any special circumstances attached to it. Obviously if Batman killed him (accidentally or even not) when Joker was in the middle of his Nth attempt on the life of Batman/Robin/a cop/anyone else, it wouldn't qualify as murder, though Batman himself probably wouldn't see it that way. Particularly because it's the Joker.
I mean, is it really out of line to respond with deadly force to someone who has actively and repeatedly tried to kill you? If he's not at least in a position of threatening at the moment, then yeah, it is.
Or in absence of that, why the Gotham County Sheriff's Department hasn't simply deputized him. It would certainly make things simpler. Batman doesn't like working within the system. It's fine if he's the one making that call, but not the other way around. Beside, most officials either deny his existence or don't trust him; Batman's PR is far from stellar. There's a lot of people who think he's insane. And there's also the issue of politics; Batman's PR stinks and they don't want to be the ones deciding that what he's doing is legal.