N.Y. Second Class Cities Law § 138
In case any such officer or member is aggrieved by the determination of the commissioner on any trial of charges, as specified in the preceding section, he may, within thirty days after the rendering of such determination, take an appeal therefrom on questions of law to the appellate division of the supreme court. An appeal taken, as prescribed herein, shall be perfected by the service of notice of appeal upon the commissioner. He shall, within ten days thereafter, make and file with the county clerk of the county in which the city is situated a complete return of the proceedings on such trial. For the use of the parties and the court on such appeal, the appellant shall cause a certified or stipulated copy of said return to be printed and issued and all the rules and statutes concerning the correction and service and use of a printed case on appeal shall as far as appropriate be applicable to the correction, service and use on appeal of said records.
N.Y. Second Class Cities Law § 138