Wyo. Const. art. 21, § 13

The governor elect of the state, immediately upon his qualifying and entering upon the duties of his office, shall issue his proclamation convening the legislature of the state at the seat of government, on a day to be named in said proclamation, and which shall not be less than thirty nor more than sixty days after the date of such proclamation. Within ten days after the organization of the legislature, both houses of the legislature, in joint session, shall then there proceed to elect, as provided by law, two senators of the United States for the State of Wyoming. At said election the two persons who shall receive the majority of all the votes cast by said senators and representatives shall be elected as such United States senators, and shall be so declared by the presiding officers of said joint session. The presiding officers of the senate and house shall issue a certificate to each of said senators, certifying his election, which certificates shall also be signed by the governor and attested by the secretary of state.