(a) Sections 62.105 to 62.116, inclusive, shall not be construed to apply to the performance of any of the classes of work therein mentioned under contracts made by property owners and duly authorized by ordinance, or under contracts made by the Board in accordance with the provisions of the Charter of this City or the general laws of the State of California, providing for the improvement of streets in municipalities.
(b) Sections 62.105 to 62.116, inclusive, shall not be construed to apply to the construction, reconstruction, or re- pair of any curb or sidewalk by any department of this City or other governmental agency which elects to perform such work using its own departmental forces where in the opinion of the City Engineer surveys, plans or inspection are not required. This exception shall not apply to the performance of any such work by the contractor engaged to perform the same by any such department or governmental agency.