Emergency services were called at 8.32pm on Friday (September 17) to reports of a road traffic collision in Ovenden.
The collision occurred on Moorside Gardens when a black Toyota collided with a parked car and two pedestrians.
One of the pedestrians, a 14-year-old boy suffered serious injuries and other pedestrian, also a 14-year-old boy, suffered minor injuries.
Both teenagers were taken to hospital for treatment.
A 28-year-old man was arrested a short time later, in connection with the incident and has since been bailed pending further enquiries.
A spokesperson for West Yorkshire Police said: "Enquiries remain ongoing and anyone with information that may assist is asked to contact police on 101 quoting log 1769 17th September.
"Information can also be given to the independent charity Crimestoppers on 0800 555 111."