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.
More top news
Christian Hickey, seven, was shot on the doorstep of his home, now he is asking Santa to help police catch the people who hurt him.
A man accused of stabbing his father to death during a row over food has been arrested by police.
The UK's biggest ambulance service is to become the first in the country to be placed in special measures.