The incident, involving a blue Renault Scenic and a white van, happened on the Wolviston Services roundabout on the A689.
Cleveland Police have said that the van made off from the scene and the Renault Scenic left the road and came to rest in a ditch.
A child in the vehicle was left with minor injuries.
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Officers believe that there were members of the public who assisted the driver of the Renault and are asking them to contact them by calling 101.
The incident took place around 4.30pm on Sunday, October 31.
Any witnesses or anyone with information is asked to contact PC Sean Parkin, from the Cleveland and Durham Specialist Operations Unit, on the non-emergency number 101, quoting incident number 185328.