The crash happened at the junction of Birkby Hall Road and Grimscar Avenue, Birkby, Huddersfield, at 9.15pm yesterday.
A West Yorkshire Police Volvo estate hit the BMW which then hit a stationary unoccupied VW Polo.
The five occupants of the BMW, all from Huddersfield, were taken to Huddersfield Royal Infirmary.
The male driver, who is in his 30s, a seven-year-old boy and a nine-month-old baby boy were released after treatment.
A woman, also in her 30s, and a nine-month-old baby boy stayed in hospital for treatment to injuries, which were not believed to be life threatening.
Two police officers were taken to hospital with minor injuries and released after treatment.
A West Yorkshire Police spokesman said: “The Force’s Professional Standards Department has been made aware and the incident has been referred to the Independent Police Complaints Commission.”
Anyone with information is asked to contact the West Yorkshire Police Major Collision Inquiry Team on 101.