The van was responding to reports of an emergency when it was involved in a collision with a Volkswagen Golf at 11am yesterday at the junction of Regent Street and Skinner Lane.
The police van, which is thought to have had its blue lights and siren on, was in collision with a dark blue Golf at the traffic lights.
Three male officers, who were in the police van, and the 18-year-old driver of the Golf were taken to hospital.
Their injuries were not thought to be life-threatening.
The incident has been referred to the Independent Police Complaints Commission (IPCC).
Motorists in the area faced traffic disruption for several hours following the crash and were advised to avoid it if possible yesterday.
West Yorkshire Police are appealing to anyone who saw the collision to contact them on 0845 6060606.