You would have to check with your states laws to be sure.
But in the State of Florida it's illegal to carry a concealed weapon on hospital grounds and that includes mental hospitals.
So I would advise you to leave your concealed weapon in your vehicle if you're visiting the hospital and if the hospital does ban concealed weapons on their property then they would likely have a sign stating they ban concealed weapons.
Either way there's really no good reason to bring any concealed weapons into a hospital so leave it in your vehicle anyway.