Police were initially called out after reports of an incident in Stanhope Road, South Shields, late on Friday night.
Two men were reported to have threatened a motorist and stolen money he had withdrawn from a cash machine at a Post Office.
As the driver tried to get away, his car overturned.
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Officers later tried to stop a car in Sulgrave Road, Washington, where an officer was knocked over as police carried out their probe into the incident.
Two men were later arrested in connection with the incidents.
A spokesman for Northumbria Police said: “Just before 11pm on Friday, September 22, police received a report that two men were seen with what is believed to be a firearm in South Shields.
“The men were seen opposite the Post Office on Stanhope Road.
“They proceeded to break the window with a crow bar and demanded a 34-year-old man’s money that he had withdrawn from a nearby cash machine.
“The male driver attempted to drive away but in doing so his car overturned.
“The offenders went on to steal cash from the car before leaving the scene.
“A few hours later, at 5.13am on Saturday, September 23, officers were carrying out search inquiries for the two men in the offending vehicle.
“They attempted to stop a car on Sulgrave Road, Washington, but as an officer approached the car drove off, colliding with the officer, who sustained a fracture to her wrist, which required hospital treatment.”
Following the incident, 31-year-old Thomas William Horn, of Bristol Avenue in Washington, has been charged with robbery and possession of an imitation firearm.
He appeared before South Tyneside Magistrates’ Court on Tuesday where he was remanded in custody to appear at Newcastle Crown Court on October 24.
A 23-year-old man also arrested following the incident has been released under investigation.