Columbia University did a recent study on mental illness and violence. There is a correlation, however correlation is not causation.
,8% of the general population is involved in violence. 3% of the mentally ill are involved in violence. But, it is complicated by other factors. If you are mentally ill, you are more likely to have numerous other issues from financial to social that contribute. If you only suffer negative symptoms of mental illness, you are less likely than the general population to be involved in violence. Forensic and Mental health experts agree that mental illness alone is not a contributing factor to violence.(above and beyond the .8%). But politics often operates on perception, and the public perception is that there is an equivalence between evil and violent, and mental illness. There is not.