Many hospitals have private security, and yes many more have actual police departments, or have actual police departments running security for them. VA being one that uses both Contracted Security, and has its own Police. Here in Indy, Eskanazi uses the Marion County Sheriff's Department's Business Special Deputies, labeled as Eskanazi Patrol, in uniform, with marked patrol cars. Also St Francis has Beech Grove Police Department as its security. In MS, the University of MS Medical Center has its own police department. Those are just a few examples.
Ive taken my dad up there a couple times and the first time I thought wow. It is almost a small city with all the buildings. Took a few to figure out where to even go to. I did notice the police cars for the place and tons of veterans.