This is going to sound like I'm trying to be funny, but I'm SO serious.
It really depends on how long they would be in jail. Like my brother for instance, who was in a mental hospital for being homicidal at one point and had threatened to kill me...if he did something HORRIBLE and I felt the need to turn him in because of it and I knew he would be locked away almost forever for the crime..I think I would tell. If he wasn't being locked away almost forever, I would be so scared that being in jail for just a while would only anger him more and he would really try to hurt me when he got out if he knew I told.
It isn't very often that he just SNAPS..but he is a very scary person when he is not in his right mind.