N.Y. County Law § 575
The office of county comptroller may be created in any county upon the adoption of a proposition submitted at a general election. The board of supervisors of its own motion by local law adopted prior to September first in any year, may create the office of county comptroller. Any such local law shall be subject to a mandatory referendum. A copy of such local law duly certified by the clerk of the board shall be filed forthwith with the board of elections of the county which shall cause the proposition to be submitted at the next general election occurring not less than sixty days after the local law is filed with the board. Upon the filing with the board of elections prior to September first in any year of a petition duly signed and acknowledged or authenticated in the same manner as a primary petition, by electors of the county equal to at least five per centum of the total vote cast for governor in the county at the last general election at which a governor was elected, praying that the office of county comptroller be created in the county, the board of elections shall cause the proposition to be submitted to the electors of the county at the next general election following the filing of the petition. The proposition shall be substantially in the following form: "Shall the office of county comptroller be created in the county of .......... " The proposition shall be submitted to the electors of the county in the manner provided by this chapter for the submission of a mandatory or permissive referendum. If the vote be in the affirmative, at the first general election held thereafter there shall be elected a county comptroller whose term shall be three years from and including the first day of January following his election. Until such office be abolished in the same manner as created, there shall continue to be elected a county comptroller for the term of three years. The county comptroller shall, before he enters upon the duties of his office, take the constitutional oath of office and execute to the county and file an official undertaking as provided in section eleven of the public officers law. Any vacancy in the office of county comptroller shall be filled by the governor in the same manner as other elective county officers.
N.Y. CountyLaw § 575