When the owners of fifty-one per cent of the frontage of property abutting a road proposed to be improved by a board of chosen freeholders under the authority of this article, petition the governing body of the municipality in which their property and the road or section thereof proposed to be improved is situate, praying that the road or section thereof be improved and paved for its entire width from gutter to gutter, and agreeing to pay the entire added cost due to the increased width of improvement and pavement, the governing body may, with the consent of the commissioner contract with the board of chosen freeholders to pay such additional cost.

The contract shall fix and prescribe the time and manner of payment of the added cost by the municipality to the county. The cost and expense so contracted to be paid by the municipality shall be assessed and collected by the municipality upon and from the real estate abutting upon the road or section of road so improved in the same manner as other assessments for benefits for improvements in the municipality.

If the improvement contemplated is being undertaken by municipal instead of county authority, the extended improvement shall be authorized by the petition herein provided for, the consent of the authorities of the municipality and the consent of the commissioner, and the additional cost shall be assessed and collected as herein provided.