From The National:
Sometimes people with such problems do commit extreme acts of violence. But so do the mentally healthy. A study published in the British Journal of Psychiatry in 2006 suggested that around five per cent of people incarcerated for murder in England and Wales were suffering from severe mental problems; that works out to about 20 homicides per year.
But even this five per cent figure is highly misleading. People with severe mental health problems (psychosis), are also far more likely than others to have problems with alcohol and narcotics. When this is taken into account, any semblance of a relationship between psychosis and violent crime vanishes.