Wyo. Stat. Ann. § 22-17-104

If the proceedings in an election contest are dismissed for insufficiency, or want of prosecution, or if the election is confirmed by the court, judgment shall be rendered for costs against the party contesting the election and in favor of the party whose election was contested. If the election is annulled and set aside for grounds stated in W.S. 22-17-101(a)(ii), (iii) or (v), judgment for costs shall be rendered against the party whose election was contested and in favor of the party contesting the election. If the election is annulled and set aside for the grounds stated in W.S. 22-17-101(a)(i) or (iv), judgment and costs shall be rendered against the county.