If such contract is authorized and executed the work shall proceed as provided therein. Upon the completion of such work if undertaken as a local improvement, the governing body of each municipality party to the agreement, shall certify to the officer or board charged with the duty of making assessments in such municipality, the cost thereof to be borne by the municipality, and such board shall make an assessment on real estate in the municipality benefited by such improvement not in excess of the benefits conferred. Such officer or board shall give the same notice and accord the same hearing and proceed in the same manner and such assessment shall be a lien and shall be enforced in the same manner as in making assessments where the improvement is made by a single municipality.