The second runs up to the car before jumping onto the hood and then again before carrying out an almost wrestling-style move that sees him landing on his bum and back onto the windscreen.
Another CCTV camera directly above the car later shows the windscreen has been smashed in the middle.
A police officer speaking in the video described how disappointed they were to find the patrol car damaged.
"We are quite disappointed that one of our vehicles were damaged," he says.
"It does take one of the vehicles away operationally - which we do rely on to keep the community safe."
Do you know any of these men? Contact Police on 105. Image / NZ Police
The officer refers to those involved as just "males", but members of the public who commented on the video - which has been shared on the NZ Police Facebook page - were not so forgiving.
"Clowns. Lowlifes," one writes.
"I think we definitely need facial recognition cameras around our towns to identify idiots like these in the future," another says.
Another poster said: "Typical losers..."
Anyone who was in the Auckland CBD that night who may have information that can help police is urged to contact authorities immediately.
Can you help? Call police on 105 or CrimeStoppers anonymously on 0800 555 111