The officers were inside an unmarked car when the vehicle was struck by a silver Toyota Yaris on Thornton Road, at the junction with Lower Grattan Street, shortly after midnight.
The Toyota was being followed by another police car - a marked patrol vehicle - when the collision happened.
The pursuit began when the driver of the Toyota failed to stop having been asked to do so by officers in the Manningham Lane area of the city at around 12.15am this morning.
The driver of the Toyota suffered minor injuries in the crash that followed. The injured police officers were taken to hospital for treatment before being released later in the morning.
An ambulance and firefighters had been called to the scene of the collision.
Three other occupants of the Toyota emerged uninjured and were arrested.
West Yorkshire Police said that due to the nature of the incident, it had been referred to the Independent Office for Police Conduct (IOPC), who attended the scene of the collision and reviewed the circumstances. The force said that the IOPC had since passed the investigation back to West Yorkshire Police.
Anyone who saw the Toyota prior to the collision or the collision itself, or anyone who has CCTV or dash cam footage, is asked to contact West Yorkshire Police on 101, or use the live chat service at www.westyorkshire.police.uk quoting log 40 of November 3.