There is no correlation real between mental illness and violence. Politicians and ignorant masses would have you believe there is, but it just isn't supported by available data. People committing violent crimes are almost always in their right mind when doing so. evil is just evil.
@Shark425 's example of a person that suddenly "nuts up" is a prime example of this ignorance. Truth be told the line between mental health and physical illness is more imaginary than real. If you deny somebody a right because of mental illness you may as well deny somebody the same right for having a cold or the flu. It is ridiculous.