Inspector Michael White said the incident began when a driver failed to stop for officers on Belfast’s Shankill Road at about 1 pm today.
He said the car was then “pursued by a trained PSNI pursuit driver” before it collided with a police landrover and another vehicle in Salisbury Avenue.
The officers sustained minor injuries.
The injured – two policemen and a policewoman – were in the landrover when the crash happened.
A 35-year-old man who was driving the car was arrested for a number of motoring offences.