Whenever any such township, city or incorporated village shall fail upon request to join in building, rebuilding, or repairing such bridge or to contribute its just share thereto, any such township, city or village desiring the building, rebuilding or repairing of such bridge may, by its township board or legislative body, as the case may be, by petition in the form of a resolution or otherwise, apply to the state highway commissioner for an order for the construction, rebuilding or repairing of such bridge and for determining the respective proportions which each township, city and village shall contribute for the construction, rebuilding or repairing of such bridge and for keeping the same in repair, as well as for deciding the kind of bridge or road to be constructed.