I'm amazed at the number of people posting here that, 1. are ignoring the OP's question, and, 2. are under the impression that hospitals are somehow immune to violent crime.
To say that someone working in a hospital has nothing to worry about or that there is no possibility of something happening is just ignorant, especially when you have no idea of what their situation is or where they work. Everyone comes to, or are brought to, hospitals - victims, victimizers, the mentally ill, people on drugs, people seeking drugs, drunks, criminals and inmates, the pillars of society as well as the dregs. There is probably more potential for violent confrontation in a hospital than most other places.
And the truth of the matter is that most facilities do not have "company police" or even uniformed security, they rely on male staff and maintenance personnel to contain things until the cops show up and they aren't necessarily readily available. The town where the hospital I work is located has one cop on duty at any given time, maybe he'll be free when 911 is called and can respond immediately, maybe not. Take all of those factors into consideration and the idea of carrying a gun for protection doesn't seem so far fetched, and certainly no less necessary than carrying anywhere else.
BTW, I'm at work right now and wearing a S&W snubby on my ankle and I have a knife in my pocket, like everyday. I just did an EKG on a very nice lady in the ER. In another room 25 feet away from her is a person awaiting commitment for attempted suicide, they shot up their trailer last night while hallucinating. That person has a history of mental illness and illegal drug use, the only security is a nurse sitting in front of the room. Nothing bad could possibly happen, right?