State tax filing

It would appear that the answer is no. 


According to Form IT-203-I, you must file a New York part-year or nonresident return if:
 You have any income from a New York source and your New York AGI exceeds your New York Statestandard deduction. You want to claim a refund for any New York State, New York City, or Yonkers taxes that were withheld from your pay.