South Yorkshire Police’s Roads Policing Team said the incident took place on Harborough Avenue in Manor on September 9 at 11.50am, when a silver Volkswagen Golf collided with a grey Volkswagen Passat.
Emergency services attended the scene and three people were taken to hospital.
The passenger of the Passat, a woman in her 80s, sustained serious injuries and remains in critical condition.
The police are now appealing for information and any dash cam footage that can assist them with their enquiries.
Anyone who witnessed either vehicle prior to the collision or who saw what happened, is asked to contact the police via 101 or through the police's new online portal here.Footage can also be emailed to [email protected]
The incident number to quote is 341 of September 9.