Is it a FEDERAL (V.A.?) Hospital?
is it a "teaching hospital"? ( grey area now we are getting into what constitutes a school)
is it private property and posted? ( signs do not carry the force of law, but as a visitor you can be asked to leave and served a no trespass order )
Federal hospital is the only one here that is an issue. Signs have no force of law, and there is no grey area for teaching hospitals, you can carry in a teaching hospital and ignore those signs. You can't enter the medical school itself as it is a school, but that is not something you will do accidentally. Tufts has the dental school but as far as I can remember it was not a thing you would just blunder into from another part of the hospital trying to go somewhere else.