The MacArthur foundation has funded a long-term study of schizophrenia and other mental health disorders and violence (and related topics) at the University of Virginia Law School. Check google for John Monahan -- the principal investigator for references. You will find a wealth of literature that should answer your questions.
People with schizophrenia are not especially prone to violence and often prefer to be left alone. Studies show that if people have no record of criminal violence before they develop schizophrenia and are not substance abusers, they are unlikely to commit crimes after they become ill.
Most violent crimes are not committed by people with schizophrenia, and most people with schizophrenia do not commit violent crimes. Substance abuse always increases violent behavior, regardless of the presence of schizophrenia. If someone with paranoid schizophrenia becomes violent, the violence is most often directed at family members and takes place at home.
