Sergeant Karl Hemmingsen, of Dunedin, said it was believed the majority of the 300 people at the party were students.
One person was arrested for minor disorder.
The party took ''some time'' to shut down because of the number of people involved, Sgt Hemmingsen said.
Several business owners guarded their doors when revellers at the party, believed to be an annual event, began vomiting and urinating on the street and climbing on roofs.
Police were called to the party at 13 Stafford St about 1.40pm after phone calls from concerned neighbours.
My Mate John's Furniture Warehouse owner John Williamson said he decided to task one of his staff with watching the store's car park when it became covered in urine.
''I hate to say it and sound like the Grinch, but it's an absolute shambles.''
Mr Williamson supported the annual Hyde St party, but believed a party in Stafford St was not appropriate.
''Our customers are disgusted.
''This is not the appropriate place for this.''
Party-goers behaved in a similar way at the event last year, including two revellers who became amorous on the furniture store's roof, Mr Williamson said.
A St John spokeswoman said they had been called to the party multiple times. Only one person was transported to Dunedin Hospital, with minor injuries.
They could not find some patients calls had been made about.
A steady flow of people came and went from the party as revellers carried intoxicated friends away from the house and others arrived.
Fourth-year University of Otago student Jake Gary, 22, of Auckland, said he believed the event went well.
''You could say it's a bit loud, but I don't think that's much of a problem.''
Otago University students Eden Edwards,19, of Auckland, and Bianca Bryan,19, of Wellington, said they were disappointed to arrive at the party as it was being shut down.
University proctor Dave Scott said he did not have complete information about the party yesterday.
''If University of Otago students have behaved poorly then they will be subject to the student code of conduct.
''Meanwhile, we will work closely with the police to ascertain full facts.''