Was he born about 1867?
Yes, inmates are listed as such in the US census, with the institution's name heading the list. Also shown are live-in-staff and their job titles.
The Pontiac State Hospital was called the Eastern Michigan Asylum, renamed Pontiac State Hospital in 1911.
A book called "Michigan Genealogy: Sources & Resources" by Carol McGinnis states that records of state mental health facilities are forever closed except to scholars/researchers with a legitimate research interest, and they must apply for access.