Upon the arrival of police, the vehicle was driven off and it evaded the police car.
It was located an hour later in one of the estate's private single-lane roads.
Cornered in a dead end, the vehicle rammed into the police car rendering it immobile and deploying its airbags, Sgt Woodbridge said.
Blocked by the police car, the vehicle then crashed through three farm gates, flinging one 20 to 25m away from its post, before crashing in a paddock and its occupants fleeing on foot.
Although the two police officers were not injured, they were "pretty shaken up'', Sgt Woodbridge said.
Extra police from Oamaru and a police dog unit from Dunedin were deployed in the area, and police were looking for the car's occupants, he said.
Sgt Woodbridge believed there were at least two people in the car.
"We may not get them straight away, but we will get them. It's just a matter of time,'' he said.
Sgt Woodbridge asked for anyone with information about the incident to contact Oamaru Police.