A video released by Tulsa police shows an officer intentionally running over and killing a 21-year-old woman after she shot at officers during a high-speed car chase.

Madison Sueann Dickson died on 18 March after officer Jonathan Grafton deliberately hit her with his patrol car as she took aim at Tulsa police chasing her.

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Dickson was wanted for her alleged involvement in a spree of gun-related crimes over the past few months, including shooting a man in the head.

After police turned up at her apartment in Tulsa, Dickson fled in a pick-up truck, closely pursued by patrol cars. She left her vehicle and presented a handgun which she fired several times at officers, according to police spokesman Leland Ashley.

"She had every opportunity to stop and turn herself in," Ashley told Tulsa World.

While she exchanged gunfire with police, officer Jonathan Grafton drove his car into her. The video shows her falling underneath the vehicle. The edited footage includes a slow down and a red circle around the suspect's hand to emphasise that she was carrying a gun.

Grafton, who has worked for Tulsa police for six years, has been on paid administrative leave since the incident.

The female driver of the pick-up truck was questioned by police and released.