I live in Bronx NY and work in new Rochelle NY do i have to pay an extra local tax?

Yes, if you live in Bronx, you need to file a New York City tax return as a resident.

thanks for replying but what I wanted to know if there is a extra local tax I should be paying because my job wasn't taking it out..I know I have to pay New York tax ,where I work is considered Westchester..

The part of Westchester that requires tax payments would be a part of the Yonkers.

@mikep1939