Please see the above response. Copied from response:
Here are the mailing addresses for mailing in your New York State Form IT-201-X, Amended Resident Income Tax Return:
If enclosing a payment (check or money order):
STATE PROCESSING CENTER
PO BOX 15555
ALBANY NY 12212-5555
If not enclosing a payment:
STATE PROCESSING CENTER
PO BOX 61000
ALBANY NY 12261-0001
Instructions to Form IT-201-X:
https://www.tax.ny.gov/pdf/current_forms/it/it201xi.pdf
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