A fourth person is in custody after the group fled the scene in a car before crashing into a parked taxi and running off.
Emergency services were called to the former hospital in Montpellier St about 10.15pm last night.
A police spokeswoman said there were initial reports that "maybe" a firearm had been seen but police had been unable to confirm that.
Investigators will visit the site this morning.
Fire and Emergency New Zealand shift manager Daryl Ball described the fire as small and was quickly contained.
The fire service was called shortly after 10pm and was still on the scene at 10.40pm.
Abandoned since 2011, the building has been gutted by two suspicious fires, one late last year and another in August this year.
The building is a hot spot for vandalism and neighbours have told the Otago Daily Times they are fed up with youths hanging around in the building late at night.
The owner, Leng Seak Loke, lives in Malaysia, and is understood to be in poor health and has stopped responding to emailed questions from neighbours.
He has told the Dunedin City Council he was making arrangements to come back to Dunedin to sort out the property.
All residents and staff at the Glamis site were transferred to the Yvette Williams Retirement Village in Highgate when it opened in early 2011.
