Upon the passage of the resolutions provided for in Section 10312, the clerk of the legislative body shall, if bonds are to be issued, transmit to the superintendent of streets, or if no bonds are to be issued, to the city tax collector the diagram and assessments adopted pursuant to Section 10312. If other than a municipal corporation is conducting the proceeding, the diagram and assessment shall be transmitted to and recorded by the corresponding officer of the entity conducting the proceeding, which officer shall be the county surveyor if a county is conducting the proceeding, and that officer shall perform the duties provided in this division for the tax collector. If neither a municipal corporation nor a county is conducting the proceeding, a certified copy of the diagram and assessment shall be recorded with the county surveyor if all or any part of the improvement district is in unincorporated territory, and with the superintendent of streets or tax collector of the city if all or any part of the improvement district is an incorporated territory.