Harvard's are.I once noticed a Harvard campus cop who didn't appear busy so I asked him exactly what authority they have.He said that they have pretty much the same authority,on University property,that municipal cops have in their city.I assume that that authority comes from state and/or Federal law.
BC and MIT also have armed police.
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I have a pal that is a retired Harvard U cop. He said his job consisted of bringing the whacked out students over to Mclean psych hospital. Harvard bought the hospital so they could hide the whacked out rich kids from the public eye.
Back in an earlier century, the campus cops where I went to college had full arrest authority on campus pursuant to state law. But they cut a deal with the county sheriff who made them deputies (with no additional pay) which gave them full county wide authority. Some smart mouthed students just off the edge of campus had to learn about that one the hard way.
Campus police are sometimes State Troopers.