The 31-year-old was hit by a black Audi S3 as he walked through an alley off on Laisteridge Lane, near Grantham Terrace in Bradford, at about 9.45pm on Wednesday, September 29,
The Audi was being pursued by the police before the crash after refusing to stop for officers.
It did not stop at the scene after hitting the man.
The man was was taken to hospital for treatment.
His condition is described as not being life threatening.
The Audi S3 was located shortly afterwards in Melbourne Place.
Police believe two men fled from the car after leaving it there.
A referral was made to the Independent Office for Police Conduct.
DI Suzanne Hall of Bradford District CID, said: “We are conducting a number of enquiries today into what has clearly been a serious incident in which a member of the public has been seriously injured by a car which failed to stop at the scene.
“Anyone who saw the collision or the car being abandoned on Melbourne Gardens, or who has CCTV or dashcam footage of the incident, is asked to contact Bradford District CID on 101 referencing log number 13210497183.
Information can also be given online at www.westyorkshire.police.uk/101livechat or anonymously to the independent Crimestoppers charity on 0800 555 111.”