No, you do not need to file a New York return.
The information below states that you don't have to file unless your New York adjusted gross income exceeds the New York standard deduction:
(Single, can't be claimed as a dependent - $7950; Married filing a Joint return - $15,950, Married filing a Separate return - $7950).
This information can be found at the link below. To see the New York standard deduction amounts, click on "New York standard deduction" (in blue print).
https://www.tax.ny.gov/pit/file/nonresidents.htm
