A 52-year-old man suffered a leg injury in the crash near the Great Northern pub on Halifax Road, Keighley.
West Yorkshire Police launched an investigation into the incident, which happened at around 11pm on Sunday, June 3.
A police spokesperson said: "The vehicle, which is described as a five door car which was possibly silver, drove off from the scene.
"Three men aged 30, 32 and 65 from Keighley have been arrested in connection with the incident and have since been released under investigation
"Enquiries by Bradford District CID have established that the driver may have been involved in a verbal altercation with the victim prior to the collision."