N.Y. High. Law § 238
The board of supervisors of a county may provide for the construction or improvement of a bridge in one or more towns of a county and at the joint expense of the county and town or towns as provided in this section. The board may by resolution direct the county superintendent to examine such bridge and report thereon, and if the board considers such bridge to be of sufficient importance to be constructed or improved as provided herein, it shall direct such county superintendent to prepare or cause to be prepared maps, plans, specifications and estimate thereon, and such county superintendent shall, subject to the direction and control of the board of supervisors, have the same powers and duties in respect to such bridge as are given to him in section one hundred and two of this chapter. Upon the completion of such maps, plans, specifications and estimate, they are to be submitted to the board of supervisors for approval, and such board shall thereupon adopt a resolution providing for the construction or improvement of such bridge in accordance with such plans, maps, specifications and estimate, or in accordance with such maps, plans, specifications and estimate as may be approved by it. The board of supervisors shall direct the county superintendent of highways to construct such bridge or may award contract for the construction or improvement of such bridge and the provisions of section thirty-eight of this chapter shall apply so far as may be to such contracts and the award, execution and fulfillment thereof. The board of supervisors shall determine the apportionment of the cost of the construction or improvement of such bridge to be borne by the county and the portion to be borne by the town or towns in which such bridge is located, or by the town or towns in which such bridge is not located but which are particularly benefited thereby. The amount to be borne by the county shall be levied and collected as a county charge and paid into the county treasury. The amount to be borne by a town shall be levied and collected as a town charge, and when collected shall be paid into the county treasury. If such bridge shall be located in a different position from an existing bridge, the board of supervisors shall acquire land for the requisite construction, and such board may also acquire land for the purpose of obtaining gravel, stone or other material when required for the construction or improvement of such bridge, together with a right of way to the bed, pit or quarry, or other place where such gravel, stone or other material may be located; and the provisions of section one hundred eighteen shall apply to the acquisition of such land as far as may be, except that the cost of such land and the expense incident to acquiring the same shall be deemed a part of the cost of the construction and improvement of such bridge under the provisions of this section. The portion of the cost of the construction or improvement to be borne respectively by the county or such town or towns may be financed, in whole or in part, pursuant to the local finance law. The construction or improvement authorized by such resolution shall be done under the supervision and direction of the county superintendent. Payments therefor shall be made from time to time by the county treasurer upon the certificate of the county superintendent indorsed by the chairman of the board of supervisors. Such bridge when completed and accepted by the board of supervisors shall be thereafter repaired and maintained at the sole expense of the town or towns in which it is located unless the board of supervisors shall apportion a share of the expense of the repair and maintenance thereof upon the county, or upon the town or towns particularly benefited. The provisions of this section shall also apply to the construction of a new bridge on a new town highway.
N.Y. High. Law § 238