N.Y. High. Law § 341-A
Wherever a county highway has been constructed at the joint expense of the state and county and the state has paid the entire cost of construction, including the share of the county, the board of supervisors of the county in which such a county highway has been constructed and the county's share of the expense advanced by the state, may, by resolution, provide for the payment to the state of its share of the cost so advanced, and appropriate and make immediately available an amount sufficient to pay the same. The clerk of the board of supervisors shall transmit certified copies of such resolution to the commissioner of transportation and state comptroller. In case there is due to the county a sum of money from any town located therein, the town board of the town is also authorized to appropriate its share of the cost and pay the same to the county treasurer of the county.
All moneys paid to the state pursuant to the provisions of this section shall be deposited by the comptroller with the department of taxation and finance to the credit of the highway improvement fund, from which fund the said moneys so advanced to said counties were originally taken, and may be expended for the construction of state highways in any county or counties designated by the commissioner of transportation. The term "county highway" shall mean any highway constructed at the joint expense of the state and county classified or referred to as a county highway under former provisions of this chapter.
N.Y. High. Law § 341-A