The crash happened at about 3.20 on Sunday, March 24 on the A63 Selby bypass, at the roundabout with the A10401.
It involved a grey Hyundai Tuscon and a white Vauxhall Corsa.
The white car did not stop at the scene and drove off leaving the two people in the Hyundai seriously injured.
A 44-year-old man from Thorne, Doncaster, was arrested later that day.
He was arrested on suspicion of drink driving, dangerous driving, failing to stop for the police and failing to provide a specimen for analysis.
Police have released him under investigation while enquiries continue.
Anyone who witnessed the collision is asked to contact North Yorkshire Police on 101, quoting reference 12190053067.