N.Y. PBO Law § 13

§ 13. Notice of neglect to file oath or undertaking. The officer or\nbody making the appointment or certificate of election of a public\nofficer shall, if the officer be required to give an official\nundertaking to be filed in an office other than that in which the\nwritten appointment or certificate of election is to be filed, forthwith\ngive written notice of such appointment or election to the officer in\nwhose office the undertaking is to be filed. If any officer shall\nneglect, within the time required by law, to take and file an official\noath, or execute and file an official undertaking, the officer, with\nwhom or in whose office such oath or undertaking is required to be\nfiled, shall forthwith give notice of such neglect, if of an appointive\nofficer, to the authority appointing such officer; if of an elective\nofficer, to the officer, board or body authorized to fill a vacancy in\nsuch office, if any, or if none and a vacancy in the office may be\nfilled by a special election, to the officer, board or body authorized\nto call or give notice of a special election to fill such vacancy;\nexcept that the notice of failure of a justice of the peace to file his\nofficial oath, shall be given to the town clerk of the town for which\nthe justice was elected.\n