The incident occurred around 1:30 p.m. Saturday.
It happened near the intersection of Greene and West Wyneva streets.
Witnesses say the car being chased sped down the busy street, knocking over tables and grills, but fortunately, no one was hurt.
Police say a police car followed, but at a slower pace and sounded sirens advising people to move to the sidewalk.
Some neighbors say the paddy wagon was going fast, as well.
According to the residents at the block party, the chase continued on, as did the block party.