N.Y. PBO Law § 37

§ 37. Notice of existence of vacancy. When a judgment shall be\nrendered by any court convicting an officer of a felony, or of a crime\ninvolving a violation of his oath of office, or declaring the election\nor appointment of any officer to be void, or that the office of any\nofficer has been forfeited or become vacant, the clerk of such court\nshall give notice thereof to the governor, stating the cause of such\nconviction or judgment.\n Whenever a public officer shall die before the expiration of his term\nof office, or shall cease to be a resident of the political subdivision\nof the state or a municipal corporation in which he is required to be a\nresident as a condition of continuing in the office, the county clerk of\nthe county in which such officer shall have resided immediately prior to\nsuch death or removal, shall immediately give notice of such death or\nremoval to the governor. If the governor is not authorized to fill any\nvacancy of which he shall have notice, he shall forthwith give notice of\nthe existence of such vacancy to the officer or officers, or to the body\nor board of officers authorized to fill the vacancy, or if such vacancy\nmay be filled by an election, to the officers authorized to give notice\nof such election.\n