N.Y. Elec. Law § 6-164
Enrolled members of a party entitled to vote in the nomination of a candidate for public office or the election of a candidate for party position in a primary election of such party, and equal in number to at least the number of signers required to designate a candidate for such office or position may file with the officer or board with whom or which are filed designating petitions for such office or position a petition requesting an opportunity to write in the name of a candidate or candidates enrolled in such party, who need not be specified, for such office or position. Upon the receipt of such a petition, such office or position shall be deemed contested and the primary ballots of the party shall afford an opportunity to vote thereon. Requests for an opportunity to write in the names of candidates for two or more offices or positions may be included in the same petition. Such petitions shall be subject to objections and court determination thereof in the same manner as designating petitions so far as the provisions therefor are applicable. All required notices shall be served on the members of the committee named in the petition, and such committee shall have capacity to bring a proceeding under this chapter as if such committee was a candidate named on a petition. A signature to a petition for an opportunity to ballot in primary elections made earlier than sixteen days before the last day to file designating petitions for the primary election shall not be counted.
N.Y. Elec. Law § 6-164