The county board, with the approval of the corporate authorities in the case of a municipality with a population of over 500, and in its own discretion in the case of a municipality with a population of 500 or less, may construct or maintain with county funds a highway or street, or part thereof, lying within the corporate limits of any municipality within the county, to connect or complete a county highway located to the corporate limits of such municipality.
605 ILCS 5/5-408