The plot reminds me of the film "Shutter Island." It turns out the main character was a patient at a mental hospital. You could also say "in mental hospital" if the patient was currently in the hospital.

Yes, although I would combine these sentences with “where” unless your second sentence is not referring to Shutter Island, then it’s fine as is.

The plot reminds me of the film "Shutter Island". It turns out that the main character was a patient from a mental hospital.