Literally (in schools, the military, etc): A pass that exempts the bearer from normal duty so they can go to hospital.
Figuratively (1): A Catch-22
] situation which will inevitably lead to a person being badly hurt, humiliated or otherwise up shit creek
Figuratively (2): In sports, a dangerous pass of the ball that may result in injury to the receiver.
Drill Instructor: Private, why are you out of the barracks?!
Private: Sir, I have a hospital pass... oohhh...
Drill Instructor: I see, that would explain all the blood spraying from your neck. NOW, STOP MOANING YOU PANSY! AND SAY SIR WHEN YOU DO!
Bill: I hear you just got assigned the Smith tax account.
Joe: Yeah, that thing is a nightmare. The IRS are investigating the company and I am probably going to be called before a grand jury.
Bill: Holy shit! That account is a hospital pass.
Doctor: So, how did you break your nose?
Private: I was playing football and the ball was passed to me.
Doctor: That doesn't sound dangerous.
Guy: Yeah, but the ball smacked directly into my face at 200 miles per hour.
Doctor: Sounds like a hospital pass. Ha ha ha ha!
Guy: Can I have another doctor?