Whenever any street in any town, having a population of less than one thousand persons, forms an extension of a county road of the county in which such town is located, and where the board of county commissioners of such county and the governing body of such town, prior to the commencement of any work, have mutually agreed and each adopted a resolution setting forth the nature and scope of the work to be performed and the share of the cost or labor which each shall bear, such county may expend county road funds for construction, improvement, repair, or maintenance of such street.