N.Y. Elec. Law § 11-300
A voter may deliver to the inspectors of election of the election district in which he is registered, or to the board of elections, at any time during the period in which an application for early mail or absentee ballot may be so delivered pursuant to the provisions of this chapter, a written statement of religious scruples against voting at a polling place located in a premises used for religious purposes. In the event the polling place for any such voter's election district shall be located in a premises used for religious purposes, the board of elections shall permit such voter to cast a special ballot, at an office of such board of elections, not earlier than one week before the election and not later than the close of the polls on election day. Such ballots shall be retained at the board of elections and cast and canvassed pursuant to the provisions of section 9-209 of this chapter.
N.Y. Elec. Law § 11-300