In its discretion, the board of an authority may file a petition at any time in the district court in and for any county in which the authority is located wholly or in part praying for a judicial examination and determination of any power conferred to the authority, any revenue-raising power exercised or to be exercised by the authority, or any act, proceeding, or contract of the authority, whether or not such contract has been executed. Such judicial examination and determination shall be conducted in substantially the manner set forth in section 32-4-540, C.R.S.; except that the notice required shall be published once a week for three consecutive weeks and the hearing shall be held not less than thirty days nor more than forty days after the filing of the petition.