It depends on whether you made any money in New York. if not, then you don't have to file a part-year NY return.
File a return if you have income from a New York source and your New York AGI (Federal amount column) is more than your New York State standard deduction.
Single and you marked item C No ......................... 8,000
Married filing joint return ........................................ 16,050
Married filing separate return ................................. 8,000
Head of household (with qualifying person) ........... 11,200
Qualifying widow(er) .............................................. 16,050