Expenses incurred by one county, on account of a mentally ill and dangerous person or a dangerous sex offender as defined in section 83-174.01 whose legal settlement is in another county of the state, shall be refunded, with lawful interest thereon, by the county in which the mentally ill and dangerous person or dangerous sex offender has his or her legal settlement. Such expenses shall be presented to the county board of the county sought to be charged, which shall allow and pay them the same as other claims. Whenever a patient of any facility over which the Department of Health and Human Services has control has been adjudicated a mentally ill and dangerous person or a dangerous sex offender as defined in section 83-174.01 and committed to a state hospital for the mentally ill, and the expenses of the adjudication and commitment have been paid by the county in which the institution is located, the county clerk of that county shall certify the total amount of the expenses thus incurred to the Department of Health and Human Services. The department shall audit the expenses so certified and shall file a statement of the amount found due with the Director of Administrative Services, and a warrant shall be drawn on the General Fund in favor of the county from which the mentally ill and dangerous person or dangerous sex offender was committed.