Option 1: If you don't owe New York income taxes and don't expect a refund by the deadline, you don't need to file a New York tax extension. However, if you expect a refund, you must file or e-file your New York tax return to receive it.
Option 2: If you've e-filed for a federal extension and don't owe New York income taxes or expect a refund, your accepted federal extension automatically extends your New York state tax deadline, so you don't need to file Form IT-370.