N.Y. Alt. County Gov't Law § 654
Any elector of the county may file with the clerk of the board of supervisors advance notice of his intention to prepare, circulate and file a petition for the submission of any question authorized by this chapter. Any such notice shall specify the alternative form of county government proposed, together with any variations and shall be accompanied by a deposit of twenty-five dollars. If the board of supervisors shall have adopted a resolution initiating a proceeding for the adoption of an alternative form of county government, with or without variations, within ten days after the filing of such an advance notice, then and in that event such advance notice shall have no further force and effect and the twenty-five dollars deposited shall be refunded to the person making the deposit. In the event that no such resolution is adopted by the board of supervisors within such period of ten days after the filing of such an advance notice, then and in that event if one-third of the number of signatures required for the submission of the question are filed with such clerk within twenty days and the remaining two-thirds within forty days after the filing of the notice, the twenty-five dollars shall be refunded to the person making the deposit and no other petition or advance notice shall be filed or accepted for filing, or resolution of the board of supervisors adopted, for the submission of any question under this chapter, until the question proposed in the advance notice shall have been submitted to the electors of the county in accordance with the provisions of this chapter. The several parts of the petition filed with the clerk of the board of supervisors under this section, when complete, shall constitute one petition, which shall be deemed to be filed for the purposes of this chapter on the date the last portion is filed. If the required number of signatures is not filed within the twenty day period, or the forty day period aforesaid, the notice of intention to file a petition shall be deemed withdrawn and shall have no further force or effect and the deposit of twenty-five dollars shall be paid into the general fund of the county treasury.
N.Y. Alt. County Gov't Law § 654