N.Y. Second Class Cities Law § 18
No person elected or appointed to a city office shall enter upon or continue in the discharge of the duties of his office until he shall have executed and filed with the city clerk the official undertaking, if any, required to be given and the same shall have been approved as to its form and validity by the corporation counsel and as to the sufficiency of the sureties by the mayor. All such undertakings shall be recorded in the office of the city clerk. In addition to the city officers required in this chapter, or otherwise by law, to give official undertakings, the common council may require any other city officer to give an official undertaking in such penal sum and with such conditions and sureties as it shall direct and approve. It may also, in a proper case, require an undertaking of any officer in addition to that required by law. The mayor shall examine the sufficiency of the proposed sureties of any officer or person from whom an official undertaking is required and may require such sureties to be examined on oath as to their property qualifications and liabilities. The deposition of each surety shall be reduced to writing, subscribed by him, certified by the officer administering the oath and annexed to and filed with the undertaking. In case any city officer shall fail to file the required official undertaking, if an elective officer, within thirty days after receipt of his certificate of election, and if an appointive officer, within fifteen days after receipt of notice of his appointment, the office shall be deemed to be vacant and the vacancy shall be filled in the manner herein provided for the filling of a vacancy therein happening otherwise than by expiration of term. The official undertaking of a city officer shall not be a lien upon real estate owned by him or the sureties on such undertaking.
N.Y. Second Class Cities Law § 18