First, you should verify what you have been credited for paying and what taxes have been applied. In the NY state return, assuming you have already gone through the interview, on the summary page "Update" "Your NY numbers" there you will see what withholding for NY and NYC that you have been credited with. You will also see if any NYC taxes were applied. If there were, go back to the summary page and "Update" the "NYC Residency" topic. Be sure your non-residency period is correct; especially if non-resident the entire year.
If you haven't gone through the NY state interview yet, do that, being sure to pay attention to the NYC residency area and then the NY numbers area.
The withholding numbers come from your W2 entries in the Federal "Wages & Income" section. The form W2 boxes 16-20 show the state and local incomes and taxes withheld. Correct those, if needed.