If NYC tax was withheld in error, the tax is refunded on the NY return. NYC tax is a component of the New York State return.
NYC tax withholding is recorded as a payment. If you indicate that you did not live in the city, then no tax is added to your New York State return. No tax due and withholding of NYC tax means the whole thing comes back to you on the NYS return.
Make sure you enter the city withholding on the W2, choosing NY as "Associated State".
