The board of trustees of a village may, by resolution, petition the commissioner of transportation for the construction or improvement of a highway to connect streets or highways within the village which have been paved or improved with state highways which have been heretofore built under the provisions of chapter one hundred and fifteen of the laws of eighteen hundred and ninety-eight, and the acts amendatory thereof. If in the judgment of the commissioner of transportation public convenience requires the construction or improvement of such connecting highway, the commissioner shall cause plans, specifications and estimates to be prepared, and shall cause the same to be transmitted to the board of supervisors of the county wherein such highway is situated. The board of supervisors may thereupon take action on such plans and specifications and adopt a resolution relating to such construction or improvement. Notwithstanding any other provision of this chapter, the cost of such construction or improvement shall be borne and payment thereof shall be made in the manner as provided for in section two hundred and sixty-four. A certified copy of such resolution shall be filed in the office of the department of transportation. The construction or improvement of such connecting highway shall then be taken up in the order and manner provided in section two hundred and sixty-one for the construction or improvement of state highways. If it is desired to construct or improve any portion of such a connecting highway at a width greater than that provided for in the plans and specifications therefor, or if a modification of such plans and specifications is desired by which the cost thereof will be increased, the board of trustees of the village shall proceed as in section forty-six to secure such a modification of the plans and specifications as will provide for such desired construction. The provisions of such section shall apply in like manner to the connecting highway to be constructed or improved as provided in this section. The provisions of this act shall not prevent the improvement by state aid under the statute as it existed prior to the passage of this act, of streets in cities of the second and third class, where, prior to the passage of this act, highway numbers had been assigned as provided by article 12 (State Routes)article twelve of this act; nor shall the provisions of this act prevent the improvement in such cities of streets heretofore petitioned for and approved in cases where the proposed improvement of each street does not exceed one and one-half miles in length; but the total mileage of all such streets not exceeding one and one-half miles in length shall not in the aggregate exceed four miles. Wherever plans for such improvement in a city of the second class have been approved and a highway number assigned, and the work is ready for contract as hereinbefore described and the common council of such city has appropriated and made available the city’s share of the cost of such improvement, the city treasurer of such city is hereby authorized, empowered and directed to deposit such moneys with the state comptroller in the same manner as is provided by this section with regard to the improvement of village streets.