It depends -
According
to the NY Department of Revenue -
If you are a New York State nonresident you must file Form IT-203, Nonresident and Part-Year Resident Income Tax Return, if you meet any of the following conditions:
So if you are a US citizen, you are filing a US income tax return, you have NY sourced income as a nonresident of NY and meet the NY state filing requirement, then you do need to file an NY nonresident state income tax return.
You can add a return for NY under the state taxes tab.
Just
follow the TurboTax guide when working on your states (remembering to do your
nonresident state return first) and TurboTax will do all the calculations and
credits to your resident states return.
Here
is additional information about filing in multiple states (select "see
more answer" to view the entire attachment)
https://ttlc.intuit.com/replies/3300797