When the owners of a majority of the lands liable to be assessed in any special assessment district, or in any part of the City which may constitute a special assessment district, petition the City Commission for any public improvement except sewers, the Commission shall order such improvement to be made. In other cases public improvements shall be made at the direction of the Commission. When the Commission shall determine to make any public improvement, including repairs, and defray all or part of the cost by special assessment, it shall so declare by resolution, stating the improvement and what part or portion of the cost thereof shall be paid by special assessment, and what part, if any, shall be appropriated from the general fund of the City, or from any specific fund, and shall designate the district or lands and premises upon which the special assessment shall be levied.