It happened at about 2.45pm on the A64 York Road on Saturday, December 14.
A silver BMW car, which was travelling in the direction of Leeds, crashed with a white Hyundai i20 car, which had been travelling in the opposite direction towards York.
The Hyundai was then crashed with a grey Skoda Superb car which was travelling in the direction of Leeds.
The BMW continued along the road before crashing with a grey Vauxhall Mokka car.
The 41-year-old driver of the BMW was seriously injured.
She remains in hospital.
Two children, aged six and eight, who were passengers in the BMW, were also injured.
The driver of the Vauxhall, a 44-year-old woman, was also seriously injured and taken to hospital.
Officers are appealing for witnesses and anyone with dash-cash footage to come forward.
They would also like to hear from anyone who witnessed the vehicles involving driving in the area prior to the collision.
Anyone with information should contact the Roads Policing Unit on the online chat service or by calling 101, quoting reference 13190639411.