Wyo. Stat. § 1-14-119
If a nonresident of the state or a partnership suing in its company name brings an action, the plaintiff must furnish sufficient security for costs approved by the clerk. A surety's obligations are complete by his endorsing the summons or complaint. The surety is bound for the payment of all costs adjudged or taxed against the plaintiff in the court in which the action is brought or in any other court to which it may be carried, whether he obtains judgment or not. The nonresident plaintiff may deposit with the clerk of court as security for costs in the case such sum of money as the clerk deems sufficient for the purpose. Upon motion of the defendant, the court may require the deposit to be increased, that personal security be given or that the nonresident plaintiff pay all costs as fast as they accrue.
W.S. 1-14-119