Only residents of New York City pay New York City income tax. However, if you are not a resident of New York City but you work for the City of New York, in most cases you must make Section 1127 payments, which will be taken out of your pay, and you have to file Form NYC-1127 in addition to your New York State tax return.
Here are a couple of references.
New York City, Yonkers, and MCTMT
Personal Income Tax & Non-resident NYC Employee Payments
