N.Y. Elec. Law § 4-138
The board of elections in each county, outside of the city of New York, on or before the fifteenth day of December and not earlier than the first day of October, in each year, shall certify to the clerk of the legislative body of the county, the total amount of the expenses of such board of elections, including salaries for the preceding year, and, if the legislative body of any county shall so direct, shall certify to such clerk the portions of such expenses which under provisions of law are to be borne by any city or cities in said county and the portion thereof which is to be borne by the rest of such county. Whenever any additional expenses either for salaries or supplies in addition to the regular county-wide primary and election expenses are incurred by a board of elections incidential to any election in any city, town or village, such board of elections shall certify to the county legislative body a detailed statement of such expenses.
N.Y. Elec.Law § 4-138