Wyo. Stat. § 1-15-502

(a) In addition to garnishment proceedings otherwise available under the laws of this state, in any case in which a money judgment is obtained in a court of competent jurisdiction the judgment creditor or his assignees shall be entitled, in accordance with this article, to have the clerk of the court issue a writ for continuing garnishment against any garnishee who is an employer of the judgment debtor. Issuance of a writ of execution is not a prerequisite to issuance of a writ of continuing garnishment. To the extent that the earnings are not exempt from garnishment, the garnishment shall be a lien and continuing levy upon the earnings due or to become due to the judgment debtor at the time the writ of continuing garnishment is served on the garnishee.

(b) Subject to the provisions of W.S. 1-15-504, garnishment pursuant to subsection (a) of this section shall be a lien and continuing levy against said earnings due until such time as the employment relationship is terminated, the underlying judgment is vacated, modified or satisfied in full, the writ is dismissed, or ninety (90) days have expired since service of the writ, whichever is sooner. A continuing garnishment may be suspended for a specified period of time by the judgment creditor upon agreement with the judgment debtor. The agreement shall be in writing and filed by the judgment creditor with the clerk of the court in which the judgment was entered and a copy of the agreement shall be delivered by the judgment creditor to the garnishee.

(c) Continuing garnishment pursuant to this article shall apply only to proceedings against the earnings of a judgment debtor who is a natural person.