If the district court requests or orders the Department of Human Services to perform any investigation or study involving the custody, placement, adoption, or other pertinent matter, with regard to a child or children with whom the Department is not otherwise involved, the Department may charge a reasonable sliding scale fee, subject to standards promulgated by the Commission for Human Services. The court shall specify the party or parties responsible for payment of such a fee. Failure to obey the order to pay the fee may be punished as contempt. The Department may also recover the fee as is provided by law for the recovery of a debt. The investigation, or study filed with the court, is subject to the sovereign immunity of the state and its employees.