In some cases patients kill other people, typically members of their own family, and then kill themselves.
It’s obviously not possible to determine their actual state of mind with absolute certainty, but the very act of killing others and then committing suicide is probably evidence enough of some level of mental disturbance.
Studies from Australia estimate that more than 90% of such suicides after homicide are mentally disordered at the time of the offence.
There are about 30 such cases in Britain each year.
The police will investigate but as there is no surviving perpetrator there is no one left to prosecute. In such cases the Coroner will hold an inquest to investigate the circumstances of the case. (See Coroner’s Courts)
If the perpetrator was a recent patient of the mental health trust, then a formal independent investigation should still be held.
As cases like this don’t come to court, they also don’t feature in official statistics of homicides by the mentally ill (which just records convictions).
The Australian study is:
Milroy, C.M., Dratsas, M., & Ranson, D.L. Homicide-suicide in Victoria, Australia. American Journal of Forensic Medicine & Pathology, (1997). 18, 369 – 373.
Figure of 30 cases a year in Britain is from:
Flynn et al; Homicide followed by suicide: a cross-sectional study. Journal of Forensic Psychiatry and Psychology, Vol 20, Issue 2, (April 2009), pages 306 – 321
See also various reports from the National Confidential Inquiry into Suicide and Homicide by People with Mental Illness