Any municipality joining in the making of any public improvement, as above provided, may assess its portion, or any part thereof, of the cost of any such improvement, upon property located in such municipality to the same extent, and in the same manner, as it might do if such improvement were entirely located within its own limits. The determination as above provided by the legislative body of a municipality as to its portion of the cost of any such improvement shall be a legal basis upon which to spread an assessment against any property benefited by such improvement.