If a district judge or magistrate orders the confinement or detention of any person under the preceding section 20-604, Idaho Code, in a jail or confinement facility in which there is no agreement as to the daily costs of confinement or detention, then any governmental unit or agency involved may apply by petition to the district court of the county in which such jail or confinement facility is located to determine the direct and indirect costs of confinement per person per day at the jail or facility. Such petition shall be filed with the district court and a copy thereof served upon the board of county commissioners or clerk thereof of the county or counties to be affected thereby, which county or counties shall be denominated as the respondent. Such respondent shall thereafter be allowed twenty (20) days to appear and plead to said petition. The determination of such costs shall be made by a district judge sitting without a jury in the same manner as other civil actions under all rules of procedure for district courts of the state of Idaho. Upon the final determination of the petition by trial or otherwise, the district court shall enter a decree binding upon all parties thereto for all persons then confined from said county or counties joined in the petition, stating the dollar amount of the confinement or detention costs per person per day which shall be paid by any such county confining or detaining persons in the jail or facility pursuant to a court order made under section 20-604, Idaho Code. Such decree shall have the force and effect of a final judgment, but the district court shall have continuing jurisdiction to vacate or modify such decree upon a material change of circumstances affecting such costs.