(a) If the judgment debtor shows the district or superior court of the county in which the judgment is filed that an appeal from the foreign judgment is pending or will be taken, or that a stay of execution has been granted, the court shall stay enforcement of the foreign judgment until the appeal is concluded, or until the time for appeal expires, or until the stay of execution expires or is vacated, upon proof that the judgment debtor has furnished the security for the satisfaction of the judgment required by the law of the state in which it was rendered.

(b) If the judgment debtor shows the district or superior court of the county in which the judgment is filed any ground upon which enforcement of a judgment of that court would be stayed, the court shall stay enforcement of the foreign judgment for an appropriate period, upon requiring the same security for satisfaction of the judgment which is required in this state.