The unmarked police vehicle was travelling along the Wetherby Road in Harrogate, through the Woodlands junction, when the collision happened.
A police officer was taken to hospital with minor injuries.
The woman driving the Seat Altea was checked over by paramedics at the scene and not believed to be injured.
Witnesses are asked to contact North Yorkshire Police on 101, option 1 and speak to the Force Control Room.
Please quote reference number NYP-17112016-0281