The accident happened at East 162nd Street and Washington Avenue in the Morrisania section.
Police say that at about 3 p.m., officers saw a vehicle commit a traffic violation.
When they tried to pull the car over, the driver attempted to flee, ran a red light, and T-boned a vehicle, then hit another vehicle.
Five people were inside the first vehicle that was struck and one was in the second. All were hospitalized with minor injuries.
Two people in the car that was being chased were taken into custody. A 20-year-old man was charged with gun possession and a 29-year-old is being questioned.
One more person is still being sought.
Police say a gun was recovered at the scene.
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