The incident happened in Newtownards last night.
A police spokesperson said: “Officers were responding to a report of domestic violence in Donaghadee shortly after 11pm when they observed a car, believed to have been involved, travelling on the Movilla Road into Newtownards.
“The car failed to stop for police when signalled to do so and struck the police vehicle a number of times as it made off.
“Two officers who were in the police car at the time sustained non life-threatening injuries as a result.
“Police located the car a short time later in the Drumhirk Avenue area of Newtownards and the suspects – a 26-year-old female and a 27-year-old male – were arrested on suspicion of a number of offences.”
Both suspects are in custody at this time.