Wyo. Stat. § 1-28-103
The injunction may be granted at the time of commencing the action, or at any time before judgment, by the district court or a judge thereof, or in the absence from the county of the judge, by the court commissioner of the county, when it appears by affidavit of the plaintiff or his agent that the plaintiff is entitled thereto. When an injunction has been vacated during the pendency of the action in the district court, and an appeal is taken to the supreme court from the judgment or final order after trial in the district court, an injunction may be granted at any time before judgment or final order in the supreme court by a judge of the supreme court, when it appears to the court or judge by affidavit of the party or his agent that the party is entitled thereto. Upon like proof, an injunction may also be allowed by the supreme or district court or by a judge of either as a temporary remedy, during the pendency of a case on error or appeal.
W.S. 1-28-103