N.Y. Elec. Law § 5-403

§ 5-403. Rejection of ballot of unqualified voter; notice of action by\nboard. If the ballot of any person, voted in an affidavit envelope in\nthe manner prescribed by this chapter, is rejected under the provisions\nof this chapter on the grounds that such person is not a qualified voter\nof the election district wherein he or she sought to vote, or is not\nduly enrolled in the party in whose primary he or she sought to vote and\nif such person has completed the application for registration and\nenrollment or change of enrollment on such affidavit envelope, the board\nof elections shall process such an application in the same manner as\nother applications for registration and enrollment or change of\nenrollment. The board of elections shall immediately notify such person\nby first class mail directed to the address given in his or her\naffidavit, of the rejection of his or her ballot, together with the\nreason therefor and, if such person has not completed the application\nfor registration by mail, the appropriate information on the times and\nplaces where he or she may register, re-register, enroll, or change or\ncorrect his or her enrollment. Where appropriate, a form of application\nfor personal registration by mail shall be included with such notice.\n