I went to two private universities (one small and in a rural area; the other large and in a major city) that had their own police force. Their officers were better trained, more accountable and more professional in interacting with the public than the notorious, local police were. They deterred crime by being present, visible and empowered to arrest. And they actually investigated crimes that local police would merely report, such as theft and date rape.
I recently asked a Johns Hopkins undergraduate leader who is opposed to having police at the university to name a single private university with its own police, where a majority of students, faculty, staff, parents or visitors actually wanted to disband their police force and deal with the scarce, overworked and unfriendly local police, instead.