Police are investigating the circumstances surrounding the incident in West Brighton at about 11 p.m.
The police cruiser collided with another vehicle at Forest Avenue and Broadway. The impact pushed the police car into a bus stop where an elderly woman was standing.
The 72-year-old woman suffered injuries to her leg and was taken to Staten Island University Hospital in stable condition.
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The officers were taken to Richmond University Medical Center with neck and back pain. The driver of the other vehicle refused medical attention.