The current issue of Psychiatric Services has several interesting articles examining the nexus between mental illness and crime.  Here are just a few (subscription needed):

From Characteristics and Experiences of Adults With a Serious Mental Illness Who Were Involved in the Criminal Justice System:

The findings of this study confirm that many individuals with a serious mental illness spend time in jail and are frequently rearrested. The characteristics of individuals who have elevated risks of misdemeanor arrests and of spending time in jail associated with these arrests are somewhat different than those of individuals who have elevated risks of felony arrests. Being male, being homeless, having an involuntary psychiatric evaluation, and not having outpatient mental health treatment in the previous quarter independently increased the odds of subsequent misdemeanor arrests and of additional days in jail. On the other hand, being black, being in a younger age group, having a nonpsychotic diagnosis, and having a co-occurring substance use disorder diagnosis were all independently associated with felony arrests. An involuntary psychiatric evaluation and the lack of outpatient mental health services in the previous quarter also increased the odds of a felony arrest, but the associations were not nearly as strong as they were for misdemeanor arrests. Because felonies typically result in longer incarcerations, it is not surprising that, with the exception of psychiatric diagnosis, all variables that increased the risk of felony arrest also increased the risk of additional days in jail.

From The Impact of Mental Illness Status on the Length of Jail Detention and the Legal Mechanism of Jail Release: 

Overall, the lengths of jail stays were found to be strikingly similar among persons with a diagnosis of a serious mental illness and those without such a diagnosis. Regardless of mental illness status, at least 50% of persons were released from jail within 30 days of entering. Furthermore, nearly half (49%) of those with serious mental illnesses had relatively unpredictable releases. Many such releases occurred after shorter incarcerations, typically with little or no notice, and an additional 8% left the jail for state sentences or incarceration in a state or other county facility.

The issue has many other good articles as well.