Henrik

As far as I know, yes. Innocents never have a reason to shoot detectives because they are 100% guaranteed to be on your side. If they are acting like a douche that's a different story, but if YOU are acting suspicious enough for the detective to want to kill you (with legitimate reason), then it's your fault, and you don't have the right to shoot back.

If he is taking guesses at who it is and is like, uh, lets try this person now... Then he's being a douche and I would shoot back. But for the most part (it is entirely situational) you shouldn't kill a detective if you are innocent.