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A number of residents witnessed the incident in the central city suburb of The Wood around midday, and reported it on social media.
A police spokesperson says the vehicle was stopped for a routine check, and before the officers could speak to the driver he reversed into a police vehicle and fled.
No one was injured but the police vehicle was moderately damaged.
Another police unit followed the driver at low speed before it came to a stop at the nearby public reserve and sportsground, Neale Park.
The driver fled but was found nearby and arrested.
A 45-year-old man was due to appear in Nelson District Court tomorrow charged with various offences.