They have been examining the circumstances of the accident on Wrangbrook Lane in February in which motorist Robert Tucker, 56, died.
Mr Tucker, from the Barnsley area, who was driving a white Vauxhall Corsa van, died at the scene of the accident around 7.30am on February 19.
The 28-year-old female driver of the other car, a red Volkswagen Golf, sustained life changing injuries.
The Golf was heading towards Upton having just left the A1 southbound, while the Corsa was heading towards the A1 having travelled from the Barnsley area.
Officers are appealing for a witness they believe may have information about the collision to come forward.
PC Lindsay Pickles said: “We have been conducting extensive enquiries in to the incident and believe there is a witness who initially stopped at the scene, but left prior to police arrival.
“We would like to trace the female driver of a red hatchback who was thought to have been travelling along Wrangbrook Lane with a child in school uniform around the time of the incident.
“I would like to stress that this individual is thought to be a witness to some or all of what took place and our purpose in locating them is to assist with our enquiries."