Wyo. Stat. § 20-1-110: Marriage ceremony according to rites and customs of religious societies or assemblies.

Any religious society or religious assembly may perform the ceremony of marriage in this state according to the rites and customs of the society or assembly. The clerk or keeper of the minutes, proceedings or other book of the society or assembly wherein the marriage occurs, or if none then the moderator or person presiding in the society or assembly, shall make out and transmit to the county clerk of the county a certificate of the marriage.