Senior Sergeant Anthony Bond, of Dunedin, said police were called to Middleton Rd about 12.15pm on Tuesday.
A truck delivering gas to a commercial premises had reversed out, driving over a 62-year-old resident of the facility, Snr Sgt Bond said.
CPR and first aid was administered but the man was pronounced dead at the scene.
WorkSafe had been notified and investigations were ongoing.
The incident had been referred to the coroner, but criminal charges could not be ruled out, Snr Sgt Bond said.
On Tuesday afternoon, road cones could be seen blocking off a Genesis Energy lpg truck outside the St Clair Park Residential Centre in Middleton Rd, while police attended.
Genesis Energy external communications manager Estelle Sarney said the company was "saddened to hear of a fatality at the site of one of our commercial customers".
"We are not in a position to comment while the incident is being investigated," Ms Sarney said.
St Clair Park Residential Centre was approached for comment.
A St John spokeswoman said an ambulance and a rapid response attended the incident.
