A West Yorkshire Police spokesman said a marked police car stopped a Seat Ibiza in a lay-by on Rooley Lane for a check.
As officers got out of their car to approach the vehicle, it made off at speed along the road before colliding with the boy on a crossing close to the Asda store.
The spokesman said: "He tragically died of his injuries."
The car did not stop but continued to the Chain Bar roundabout on the M606, where it was in collision with two other vehicles.
It was later found on Westfield Lane, in the Wyke area of Bradford.