The governing body of each city in which an improvement is being made or acquired pursuant to this chapter may make all necessary rules and regulations for carrying out and maintaining the improvement, and may appoint all agents, superintendents, and engineers necessary to look after the construction and operation of the improvement. However, in any city operating under a charter framed pursuant to Sections 3 and 5 of Article XI of the California Constitution which has a board or department of public works, the powers and duties of the governing body which are stated in this section may be exercised and performed by the city board or department of public works.