If an estate or interest in an estate passes so as to be liable to taxation under this chapter, all costs of the proceedings for the assessment of the tax are chargeable to the estate as other costs in probate proceedings and, to discharge the lien, all costs as well as the taxes must be paid. In all other cases the costs are to be paid as ordered by the court. When a decision adverse to the state has been rendered, with an order that the state pay the costs, the clerk of the court in which the action was pending shall certify the amount of the costs to the director of revenue, who shall, if the costs are correctly certified and the case has been finally terminated and the tax, if any is due, has been paid, audit the claim and direct the department of administrative services to issue a warrant on the treasurer of state in payment of the costs.