(a) Prior to beginning construction on a project, the board shall provide by resolution for the construction of the project and shall also provide in the same or subsequent resolutions for the supervision of such work by a professional engineer, governmental agency or any other person designated by the board. The board may provide for the construction of the project by one of the two following methods or any combination thereof:
(1) If there exists a governmental agency with the experience, knowledge and authority to construct the project, the board may elect to enter in a contract with such agency for the construction of all, or a part of, the project or for any other service necessary or incident to the construction of the project, in which case such governmental agency shall be responsible for entering into contracts, subject to the board's approval, with such other persons as may be necessary or incident to the construction of the project; or