Jenny Newbury was hit by a marked police Ford Sierra as she crossed a road near her home in Salford, Greater Manchester, with a friend on Sunday night. The police car was carrying out a speed check on a vehicle it was following.
Jenny was taken to the intensive care unit at Manchester Royal Infirmary with serious head injuries, but died on Monday night with her parents at her bedside.
The Police Complaints Authority yesterday agreed to oversee an inquiry into the death - their third in the past fortnight involving a police car.
Police said the two girls ran into the path of the car in Trafford Road, Ordsall.
The officer at the wheel swerved to the offside lane of the dual carriageway, but was unable to avoid the collision. The PCA inquiry will want to establish the speed of the police car at the time of the accident.
Greater Manchester Police said the car was on routine patrol duties when the accident occurred at 7.20pm on Sunday, but gave no details of its speed.
An investigation is under way and the two officers in the car, both said to be deeply shocked, are to be interviewed, together with the other girl, who was uninjured.
Results of the inquiry will be forwarded to the Crown Prosecution Service to assess whether the officers involved should be charged.
Last Wednesday, a newly-wed Turkish woman died after being catapulted into the air by a police car.
Yeter Ozer, 22, was killed in front of her husband as they crossed the road near their home in Finsbury Park, north London.
Six days earlier, John Stanley, 53, died after being hit by a police car on a pedestrian crossing in Kentish Town, north London.
In both those cases the police vehicles had their flashing blues lights on but siren turned off.