Nope, the statistics don't support that assertion:
http://www.apa.org/news/press/releas...ess-crime.aspx
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1389236/
https://www.nytimes.com/2016/07/08/u...or-blacks.html
Mentally ill people are not significantly more likely to commit crimes, but are more likely to be the victims of crimes. Black people are much more likely to be the recipients of violent force even when racial disparities of crime are taken into account. Also, black people statistically receieve longer sentences for the same crimes as white people.