Troopers identified the man as 28-year-old Tremaine Jackson from Wilmington, Delaware.
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The incident began on Thursday, August 31 just before 7:30 a.m.
State police responded to the Lowe's located on Hessler Boulevard in New Castle for reports of a known fugitive shoplifting in the store.
At the scene, troopers said they saw Jackson fleeing the store with a shopping cart full of merchandise. Troopers attempted to contact him, but he ran away.
Jackson then got into a getaway vehicle, which was parked behind the business, and struck an unmarked state police vehicle while attempting to flee.
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While attempting to take Jackson into custody, officials say he did not comply with commands to stop and he physically resisted when troopers tried to remove him from the car.
Troopers say they shot Jackson when he continued to drive in a way that placed them in imminent danger.
Jackson was transported to an area hospital where he was later pronounced dead.
Two troopers were also taken to an area hospital with non-life-threatening injuries and were later released.