yeah it depends on the college. small colleges just have someone whose biggest weapon is a flashlight, and who have no official legal authority outside of college grounds. in this case, the biggest punishment they can give is a parking ticket or citation (that said though, college policy may state that after a certain number of these citations you are kicked out permanently). however, at larger universities they are certifiable police officers who can carry around guns and have every legal right to search, arrest, detain and prosecute you as any local or state cop could.
If you run, they'll chase you, think: why is he/ she running? They'll tackle you, potentially tase you. Stand your ground, know your rights. It's hard to get away from cops now a days with radios and cameras. It can still be done. Try not to put yourself in positions where you're 'forced' to run away. Think methodically.
Thats the truth right there... Running away is always stupid unless your far enough away and you have some cover... Cuz otherwise they know what you look like and your likely to get caught