N.Y. Alt. County Gov't Law § 651
Upon the filing with the clerk of the board of supervisors of a petition signed by electors of the county equal in number to at least ten per centum of the whole number of votes cast in the county for governor at the last gubernatorial election asking that a referendum be held on the question of adopting one of the alternative forms of county government authorized by this chapter, with or without variations, the board of supervisors shall cause the question to be submitted to the electors of the county in the manner hereinafter provided. Proceedings may be instituted and maintained to contest the sufficiency and validity of any petition in the manner provided in the election law, as though such petition were a designating petition. If the petition be sufficient and valid, the board of supervisors shall by resolution cause the question to be submitted to the electors of the county for approval or disapproval at the next general election occurring in an odd-numbered year and not less than sixty days after the date on which the petition is filed.
N.Y. Alt. County Gov't Law § 651