N.Y. Alt. County Gov't Law § 652
The board of supervisors of a county may by resolution duly adopted provide for submission to the electors of the county of one of the alternative forms of county government authorized by this chapter, with or without variations, at the next general election occurring in an odd-numbered year and not less than forty-five days after the adoption of the resolution; provided, however, that no such resolution shall be adopted by the board of supervisors after the initiation of a proceeding for the adoption of an alternative form of county government, with or without variations, by the filing of a petition therefor, or subsequent to ten days following the filing of an advance notice of filing such a petition, so long as the proceeding initiated by the petition or thereafter initiated pursuant to such advance notice is pending.
N.Y. Alt. County Gov't Law § 652