New York Consolidated Laws, Election Law - ELN § 4-136. Election expenses;  payment of

1. Except as provided for in subdivision two of this section, the expenses of providing polling places, voting booths, supplies therefor, ballot boxes and other furniture for the polling place for any election, including the storage, transportation and maintenance of voting machines, appliances and equipment or ballot counting devices, and the compensation of the election officers in each election district, shall be a charge upon the county in which such election district is situated, except in the city of New York where such expenses shall be a charge upon the city of New York.

2. All expenses incurred under this chapter by the board of elections of a county outside of the city of New York shall be a charge against the county and in the city of New York the expenses of the board of elections shall be a charge against such city.  The expenses incurred by the board of elections of a county outside the city of New York may, pursuant to section 3-226 of this chapter, be apportioned among the cities and towns therein, or in the case of a village election held other than at the time of the fall primary or general election, apportioned to such villages therein.

3. In the city of New York all leased or purchased equipment, supplies, ballots, printing and publications, except newspaper notices and advertisements, to be used or furnished by such board, may be procured for it by the purchasing department or agency of such city as if such board were an agency of such city.  Such board shall comply with the rules and regulations of the New York city procurement policy board and applicable state law.