Whenever the city of Aberdeen shall be liable for the payment of costs in any criminal action or proceeding in municipal or superior court, a cost bill shall be prepared and certified by the officers hereinafter mentioned, specifying the different items of cost for which the city is liable; and where witness or jury fees are included in such cost bill the name, address, per diem and mileage of each witness or juror shall be specified. In all criminal cases in the municipal court, cost bills shall be prepared and certified to by the municipal court judge. In all such criminal cases in the superior court, brought there on appeal from the municipal court, the cost bill showing all costs for which the city of Aberdeen shall be liable shall be reviewed by the city attorney. It shall be duty of the city of Aberdeen to issue to the several parties, jurors and witnesses, shown by said cost bill to be entitled thereto, their respective costs and fees to which such cost bill shows them to be entitled.