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There is no prohibition in the statutes for carry in a hospital. However, almost all of the hospitals I have seen are posted. There is no exemption for state, parish, or municipal ownership of the facility and gun buster signs carry the force of law. There are those that claim signs only mean that once asked to leave you face a trespass charge, not illegal possession of a gun, but at best it a "beat the rap, not the ride" situation and would vary from one jurisdiction/DA to another.

Hope this helps!

ETA: Another point of confusion, unrelated to hospitals, is carrying in a Class A General facility. Those are bars; restaurants that serve alcohol are given Class A Restaurant licenses. A good rule of thumb is whether the establishment is age restricted, but the Alcohol and Tobacco Commission has a web page to look up a place's certification.