The accident happened on Friday afternoon at the Compare Foods market. Authorities said none of the injuries appeared to be life threatening.
The driver told police he accidentally hit the accelerator instead of the brake while trying to park and crashed through the sliding entrance doors.
A witness told the Connecticut Post (http://bit.ly/Kq0v14) that people were trying to get out the car's way, but couldn't.
Besides three customers, the car's driver and a passenger were also hospitalized after the crash.
Police didn't immediately release the names of the driver or the victims.
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