Which criminal behaviors are common with mental illness?
There are a vareity of behaviours that become more likely with the advent of mental illness. The type of criminal behaviour may however, depend on the exact nature of the illness.
If we take Kluver-Bucy syndrome for instance, this can occur (extremely rare) after a partial surgery on the temporal lobe to alleviate epilepsy symptoms, or as a result of neurodegeneration or lesions etc. In this condition first identified in rhesus monkeys, the patient may exhibit sexual deviancy as well as hypper-orality (a tendency to eat voraciously or uncontrollably).
The late, great Oliver Sacks wrote a fascinating paper on this syndrome and its relation to the law.
Although this is a neuropsychological illness, one may infer that any time a mental illness is due to a malfunctioning brain circuit, this may lead to criminal behaviour.
Any illness that halts the full functioning of the PFC (prefrontal cortex) is likely to damage the ability to fully inhibit one's own behavour and lead to impulsive behaviour.
Impulsivity is one of the main casualties of mental illness, as is the ability to inhibit one's behaviour.