Many universities have a separate police department than the city in which they're located. This makes some sense with big schools, and even more so for large public schools (Cornell is private), since they're essentially a separate government than the city.
I teach nights at a large university with its own UPD, and they're excellent. Their officers are better trained and accustomed to the kind of law enforcement that works best with universities.
When 19yo kids are drunk, high, and loud pattying in a dorm room, they show up and ask them to tone it down and offer to arrange a free ride home for anyone instead of arresting people like the city police do in off-campus apartments.
When a student is having a meltdown, instead of shooting them they try to calm them down and arrange for them to see one of the university's counselors.
When a local creep is being a creep around the college girls, they trespass them from university grounds.
They're part of the university, but the university deans have no more influence on them than the planning director of a city has on their police department. Overall, UPD is great.
Parking services, on the other hand, can go to hell. $800 a semester for a faculty pass to still get parking tickets for daring to have my car in the lot for a specific 4 minute stretch between 6:38 and 6:42 when it's a commuter pass only lot, which I should have known because of the Cyrillic text written in invisible ink on a brochure from 1978.