N.Y. High. Law § 151
The town superintendent of any town may, with the consent of the town board, maintain and repair existing sidewalks in such town, and the expense thereof shall be a town charge. Where such sidewalks shall consist of a board walk not more than ten feet in width located on a highway less than two rods in width the town superintendent of such town may maintain and repair such board walk or renewal thereof and with the consent of the town board may replace such board walk with a walk of concrete or other suitable construction and the expense thereof shall be a town charge. The town board of any such town may by resolution, direct the town superintendent to construct a sidewalk along a described portion of any highway of the town, including county roads and state highways, in the manner and not exceeding an expense to be specified in the resolution, and the expense of constructing such sidewalk shall be a town charge, and shall be paid in the same manner as other town charges. No such sidewalks shall be built along any state highway until the state commissioner of transportation shall have made his consent thereto, pursuant to section fifty-four of this chapter, and no such sidewalk shall be built along any county road until the county superintendent of highways shall have made his consent thereto, pursuant to section one hundred thirty-six of this chapter. Nothing herein contained shall prevent the town board from requiring the maintenance and repair of such sidewalks and the removal of snow therefrom by the owners or occupants of property adjacent thereto as may be required by the provisions of any town ordinance adopted pursuant to the provisions of article nine of the town law. The provisions of this section shall not apply to towns in a county containing more than three towns and adjoining a city of the first class having a population of one million or more, except that (a) in the town of New Castle, the town superintendent, upon resolution of the town board consenting thereto, may maintain and repair existing sidewalks in such town, and the expense thereof shall be a charge against the unincorporated area of said town, and (b) in the town of Greenburgh at any annual school district meeting the majority of the voters present and voting thereat may authorize the school board of such district to petition the town board to construct, maintain and repair sidewalks fronting on its school property or specified portions thereof and pursuant to such petition the town board may by resolution direct that the town superintendent provide for the construction, maintenance and repair of such sidewalks and the cost thereof shall be assessed against the school property benefited thereby and paid by such school district and (c) in the town of Mount Pleasant, the town superintendent, upon resolution of the town board consenting thereto and authorizing the same, may construct, maintain and repair or cause to be constructed, maintained and repaired sidewalks along a described portion of any highway in the town, including county roads and state highways, providing that in the case of sidewalks along county roads and state highways no sidewalks shall be built until the consents hereinabove provided are first obtained, and the expense thereof shall be a charge against the unincorporated area of the said town.
In any town in which no village is situated, the expense of constructing a sidewalk along a described portion of any highway in the town, including county roads and state highways, as herein provided, may be financed in whole or in part as provided by the local finance law, and the construction of such sidewalks may be made by contract in the manner provided by section one hundred ninety-three herein.
N.Y. High. Law § 151