Mo. Rev. Stat. § 514.200

In all such cases, the judgment against the state or county shall not be for costs generally, but the amount thereof shall be expressed in the judgment, and no such judgment shall afterwards be amended so as to increase the amount for which it was originally entered; and, upon a transcript of such judgment, together with a certified copy of the fee bill, showing the items of cost, being presented to the state auditor or the county court, the same shall be audited and allowed.