This is, I believe, now completely a thing of the past almost everywhere, but America being rather conservative, there could be echoes of it around.
This is still the case at many universities. Offenses which would be classified as criminal (i.e. public intoxication) are handled internally by the university. From one perspective, handling the mistakes of students like this is a way of protecting the university's revenue stream, as parents often withdraw their children from the university after a criminal offense.
But then I recalled an article earlier this year about how "campus PD" have been intervening in sexual assault cases and trying to get them handled by the university instead of the justice system, where there's public record and of course publicity.
And there's no doubt that it could not have this reputation with more lenient policing than you'll see anywhere else. Certainly moreso than the policing in the inner city ghetto a mile away.
I've seen campus police consistently do nothing over drug possession issues that would, without question get jail time anywhere else in the city.
The dissonance is disturbing to me.
It might be. I just had a look around for a citation and didn't find much. However I do recall a law student finding something in the university by-laws about it (however that shouldn't overrule state law... unless it does). I found http://www.austlii.edu.au/au/journals/UWSLawRw/2002/3.html but the University of Melbourne seems to be victorian crown land (since at least 2000 http://www.legislation.vic.gov.au/domino/Web_Notes/LDMS/PubP...) rather than commonwealth crown land. I don't know enough about property and title in Victoria to make a call here.
(AFAIK, the regular police don't have any jurisdictional limits stopping them from acting within university premises, but the University of Cambridge can appoint its own additional officers.)