I want to have sex with someone who was recently discharged from a mental hospital
How long have they been out of the mental hospital?
They were released yesterday.
This sounds like you may just be taking advantage of this person.  You want to make sure they're healthy and mentally fit before having sex.  To do otherwise might mean they aren't really consenting.
Hey, they were released which means that they're healthy and able to consent.
It's true that they're healthy enough to go home, but I still don't think it would be right for you to ask them if they want to have sex right now. You should really give them some time to settle in and make sure they're ready before asking them.