It happened on Dublin Road area in Newtownhamilton area of of Newry on Thursday, 9th May.
Constable Gerry Roberts said: “We received a report of anti-social driving at 11.30 pm on Thursday night, officers attended and observed a vehicle attempting to ‘donut’.
“When officers signalled their blue lights, the vehicle attempted to make off, it collided with the police vehicle, a parked car and a female pedestrian was injured.
“The driver made off, leaving the vehicle at the scene, two officers were also injured during the incident.
“The woman was taken to hospital for treatment of her injuries which are not believed to be life threatening.
“Enquiries are continuing and we are appealing to anyone who witnessed the incident or who may have dashcam footage available to contact police on 101, quoting reference number 11 of 10/05/19.
Alternatively, information can also be provided to the independent charity Crimestoppers on 0800 555 111 which is 100% anonymous and gives people the power to speak up and stop crime.