N.Y. Elec. Law § 8-314

§ 8-314. Voting; primary election, missing enrollment record. If a\nregistered voter marked an enrollment blank, but his enrollment as so\nindicated was not entered or entered incorrectly, he nevertheless shall\nbe permitted to vote at the primary election, with the party under whose\nname he marked such blank, if he produces a certificate of the board of\nelections that he marked an enrollment blank, specifying the party, and\nthat the entry of his enrollment on the registration poll record was\nomitted or incorrectly entered by inadvertence or mistake and he is\nqualified to vote at the primary election in the party set forth in such\ncertificate. In such a case the board of elections shall issue such\ncertificate on demand. The inspectors shall then and there enter the\nenrollment on the record.\n