The male and female pedestrians were hit by a car on Stanley Road, in King Cross.
They were treated in hospital for what police described as "minor injuries".
The Courier understands these included a broken leg that required surgery and hospitalisation for one of the victims, and cuts, bruises and a bad shoulder injury for the other.
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The vehicle, which failed to stop, is believed to be a black Volkswagen Golf with a ‘10’ number plate.
Anyone who witnessed the collision, which was reported to police at 11.09am on Friday, July 22, is being asked to call the Roads Policing Unit on 101 or by using the live chat function on the West Yorkshire Police website.
Officers also want to hear from anyone who has footage that might help with their investigation.