The incident, involving a Ford Focus, a Vauxhall Adam and a Vauxhall Astra, happened at around 5:35pm at the junction of the A689 Stockton Road and Truro Drive on Thursday, May 12.
The female driver of the Vauxhall Adam was taken to James Cook University Hospital in Middlesbrough after suffering a number of injuries, including a broken ankle.
Cleveland Police said that the 32-year-old male driver of the Ford Focus was arrested on suspicion of driving offences and have asked for witnesses or anyone with footage of the incident to come forward.
A force statement read: “A 22-year-old female driver from the Vauxhall Adam suffered a number of injuries including a broken ankle and was taken to James Cook University Hospital for treatment.
“The 32-year-old male driver of the Ford Focus was arrested on suspicion of driving offences and he has been released under investigation whilst enquiries continue.
“Officers would appeal to anyone who may have witnessed the collision or may have dash cam footage of the incident or an 09 reg silver Ford Focus in the area of the A689 prior to the collision.
"Anyone with information is asked to contact PC David State on 101, quoting incident number 080105.
Footage can also be uploaded directly to https://unitedkingdom1cpp-portal.digital-policing.co.uk/cleveland/appeal/appeal-after-three-vehicle-collision-in-hartlepool”
Stockton Road was closed in both directions from Truro Drive to the area near to Cleveland Fire Brigade HQ, before reopening later on Thursday evening.