IIRC most studies put it at somewhere between 5-10% for murders - that's people who were exhibiting mental health problems at the time of the offence, it doesn't necessarily mean that they were in contact with mental health services or had a diagnosis. in my experience (i work with people with mh problems who have committed offences) a lot of them either weren't on the radar of mh or social services, or the services didn't have the resources (or inclination, in some cases) to help them when they were at their lowest point. also, people with mental health problems are 6 times more likely to be victims of violence than people without. in conclusion then, IMO it's definitely the sane people that we should be worrying about!