When a state court decides a perpetrator is mentally ill does the state then become the legal guardian of this person?

Or do they become property of the feds? Either way, does the state or federal government then have the right to run any sort of scientific tests on the perpetrators brain? Can the perpetrator deny any of this from happening?

I’m trying to figure out possible benefits to society of having the said perpetrator mentally ill. Or perhaps there is no study conducted on them?