N.Y. Elec. Law § 5-902
If a voter registration exemplar signature is not received from an applicant who submits a voter registration or pre-registration application pursuant to this title and such signature exemplar is not otherwise available from the statewide voter registration database or a state or local agency, the local board of elections shall, absent another reason to reject the application, proceed to register or pre-register and, as applicable, enroll the applicant. Within ten days of such action, the board of elections shall send a standard form promulgated by the state board of elections to the voter whose record lacks an exemplar signature, requiring such voter to submit a signature for identification purposes. The voter shall submit to the board of elections a voter registration exemplar signature by any one of the following methods: in person, by mail with return postage paid provided by the board of elections, by electronic mail, or by electronic upload to the board of elections through the electronic voter registration transmittal system. If such voter does not provide the required exemplar signature, when the voter appears to vote the voter shall be entitled to vote by affidavit ballot.
N.Y. Elec. Law § 5-902