Officers have released a CCTV image following the hit-and-run in Great Wyrley on Tuesday, November 15.
Police were called to Station Road, near Hall Lane, which involved a pedestrian and a vehicle.
A teenage boy from the local area was taken to hospital with leg injuries and has since been discharged.
The car is believed to be a black Ford Fiesta, which failed to stop at approximately 8.33am.
Witnesses who may have seen the collision or the vehicle beforehand, or anyone with relevant dashcam or CCTV footage, are asked to message Staffordshire Police on Facebook, Twitter, or call 101, quoting incident number 301 of November 15.