N.Y. Criminal Procedure Law § 460.10
1. Except as provided in subdivisions two and three, an appeal taken as of right to an intermediate appellate court or directly to the court of appeals from a judgment, sentence or order of a criminal court is taken as follows:
3. An appeal taken as of right to a county court or to an appellate term of the supreme court from a judgment, sentence or order of a local criminal court in a case in which the underlying proceedings were not recorded by a court stenographer is taken as follows:
4. An appeal by a defendant to an intermediate appellate court by permission, pursuant to section 450.15, is taken as follows:
5. An appeal to the court of appeals from an order of an intermediate appellate court is taken as follows: