Officials say 10 people were injured after the driver drove his vehicle through E. 42nd Street and Lexington Avenue at around 5:30 p.m.
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The victims were taken to Bellevue Hospital with non-life-threatening injuries.
According to police, the vehicle, a 2018 Hyundai Tucson with Illinois plates, was reported stolen from the Bronx last month.
Officers say they followed the vehicle while attempting to verify if it was the same one stolen.
The driver tried to flee from police during the attempted car stop, striking a bicyclist and then colliding with a Yellow Cab taxi before jumping the curb and striking several pedestrians.
He proceeded to drive the wrong way on Lexington, before coming into contact with another vehicle.
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The 20-year-old man was then detained by civilians and held until officers made the arrest.
He remains in custody.
The incident does not appear to have any connection with terrorist activity.
An investigation is ongoing.