It occurred on the A1079, Dunnington just after 6.30am, Tuesday 24 May and involved a Ford Focus and a green tipper wagon.
The man driving the Focus received serious injuries and was taken by air ambulance to Leeds General Infirmary. The driver of the wagon was treated at the scene for an arm injury.
Traffic Constable Lee Cobb, of the force’s Roads Policing Group, said: “I am particularly keen to speak with the driver of silver lorry which was directly behind the green truck.
“I urge them to contact me straight away as I believe that they will have vital information about the collision.
“If anyone else witnessed the collision or can help to identify the driver I ask that they contact me as soon as possible.”
If you can assist with this investigation please contact TC Lee Cobb on 0845 60 60 24 7.