When the punishment of the crime is the confinement of the criminal in a Department of Correctional Services adult correctional facility, the expenses shall be paid out of the state treasury on the certificate of the Governor and warrant of the State Treasurer and Director of Administrative Services. In all other cases the expenses shall be paid out of the county treasury in the county wherein the crime is alleged to have been committed. The expenses shall be the fees paid to the officers of the state on whose Governor the requisition is made and shall be equal to the mileage rate authorized in section 81-1176 for each mile which is necessary to travel in returning such prisoner.