The 40-year-old man was hit by a red Volkswagen Golf in Cemetery Road at the junction with Duncombe Road shortly before 12.20pm on Friday, October 5.
A West Yorkshire Police spokesman today said: "The driver of the Golf stopped the vehicle further down the road and walked up to the injured pedestrian but then left the scene without exchanging details.
"A 23-year-old man later attended at a police station and was interviewed in relation to the collision."
Now officers want to speak to any witnesses who saw what happened before or after the collision.
Call the Western Area Safer Roads Policing Unit via 101, quoting crime reference 13180497966.