Two officers were injured.
The shooting occurred on Park Avenue following a pursuit, police said.
State police said that a Bridgeport officer opened fire when the stolen vehicle accelerated in reverse and hit an officer.
Officers sustained possible minor injuries but the details are unclear, Connecticut State Police said.
The names of the driver and officers have not been released.
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The passenger was identified as Julian Fyffe, of Bridgeport, who officials said was the grandson of a city officer.
"We got in the vehicle to be a witness and to come in solidarity with the community that's asking questions", he said.
State police say Bridgeport officers stopped the stolen auto Tuesday afternoon after a pursuit. But the driver suddenly accelerated in reverse at a high rate of speed and almost dragged an officer under the auto, he said. The auto eventually stopped, and two officers tried to get the two occupants out, Perez said.
A crowd gathered at the scene Tuesday night to protest the actions of the officer who opened fire. That's when an investigating officer supposedly replied "If one of our lives is in danger, it's different". Anyone with information is asked to contact state police by texting TIP711 and any information to 274637.