N.Y. High. Law § 196
The board of supervisors of a county may, upon the petition of the board of trustees of an incorporated village, provide for the construction or improvement of a highway or section thereof, through such village, at the joint expense of the county and village. The board of supervisors shall determine the portion of the cost of the construction and improvement of such highway to be borne by the county and the portion to be borne by the village. The portion, if any, to be borne by the village shall be a village charge and the residue shall be a county charge. The amount to be borne by the county shall be provided by tax, to be levied upon the taxable property of the county and collected in the same manner as other county charges and shall be paid into the county treasury and such tax shall not be reported as a basis for state aid as provided by article six of this chapter or the county may finance all or part of its share pursuant to the local finance law. The board of supervisors may, in its discretion, appropriate and make immediately available from county funds, the portion of the moneys to be borne by the county.
The board of supervisors may designate the highway to be improved under the provisions of this section and in such case, the cost shall be borne by the county. No such highway shall be so constructed and improved through a village, except to connect a highway improved pursuant to the provisions of sections one hundred and ninety-four, one hundred and ninety-five, or article six of this chapter with a state highway, or a county road, or to connect with another town highway improved pursuant to the provisions of sections one hundred and ninety-four, one hundred and ninety-five, or article six of this chapter, or to connect a city street with a highway improved by the county or state. Such construction shall not be commenced until the portion, if any, to be borne by the village, as determined by the board of supervisors, has been deposited in the county treasurer's office of such county. The construction or improvement of a highway, as herein provided, shall be done under the supervision and direction of the county superintendent of highways or of a committee known as the highway officials of the county, to consist of the county superintendent, three members of the board to be appointed by the chairman, and the supervisor of the town in which road is being improved. Payments therefor shall be made from time to time by the county treasurer upon the certificate of the county superintendent, approved by the chairman of the board of supervisors.
A highway within a village constructed or improved as herein provided, shall be of the same width and type of construction as such town highways so improved by the aid of the county outside the village, unless a greater width or different type of construction is desired by the village. The additional expense caused by the increased width or different type or both, shall be borne wholly by the village. Any such highway, when completed, shall thereafter be repaired and maintained by the village wherein such highway is located in the same manner as all other village highways. The board of supervisors may determine that such highways be thereafter repaired and maintained under the supervision and direction of the county superintendent of highways and thereafter the amount, if any, to be borne by the village shall be paid by the village into the county treasury and the whole of such money including the share of the county and of the village, if any, shall be paid out by the county treasurer for the repair and maintenance of such highways on orders signed by the county superintendent of highways and countersigned by the chairman of the board of supervisors.
N.Y. High. Law § 196