Maybe, you only need to file a New York, non-resident return if your New York income exceeds the New York Standard Deduction for your filing status.
2019 Standard Deduction for New York
(1)Single (and can be claimed as a dependent on another taxpayer's federal return) $3,100
(1)Single (and cannot be claimed as a dependent on another taxpayer's federal return) $8,000
(2)Married filing joint return$16,050
(3)Married filing separate return$8,000
(4)Head of household (with qualifying person)$11,200
(5)Qualifying widow(er)$16,050
If you are not required to file a New York return then you do not report the amounts in Box 13, except on your Federal Return.
If you are required to file a New York return the information will flow from the Federal return to the state return.
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