The board may establish local improvement districts within the boundaries of the authority to facilitate the financing, construction, operation, or maintenance of public highways within or without the boundaries of the authority. Such local improvement districts may be established by the board whenever any area within the boundaries of the authority, in the opinion of the board, will be especially benefited by the financing, construction, operation, or maintenance of such public highway. No local improvement district shall be established by the board unless it receives a petition signed by the owners of property which will bear a majority of the proposed assessments and by a petition signed by the lesser of a majority of the registered electorate in the proposed district or one thousand registered electors in the proposed district. The method of creating local improvement districts, making the improvements, and assessing the costs thereof shall be as provided in part 6 of article 20 of title 30, C.R.S.; except that the board shall perform the duties of the board of county commissioners thereunder and the improvements shall be public highways as defined by section 43-4-503 (12).