The incident was reported at 11.09am on Friday, July 22 and is thought to have occurred a short time before, on Stanley Road, King Cross.
The pedestrians, a male and female, were treated at hospital and the female suffered serious injuries as a result of the collision.
The vehicle, which failed to stop following the collision, was believed to be a black Volkswagen Golf with a ‘10’ number plate.
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Enquiries are ongoing and officers are appealing for anyone with any information which may assist with ongoing enquiries to contact police.
In particular anyone with CCTV or dash cam footage of the VW Golf in Stanley Road around the time of the collision.
Anyone who witnessed the collision, or who has footage that will assist the investigation is asked to contact PC 970 Townsend at the Roads Policing Unit on 101, or by using the LiveChat on the West Yorkshire Police website.