Wyo. Stat. § 15-3-201
The mayor is entitled to sign or veto any ordinance passed by the governing body and to sign or veto any order, bylaw, resolution, award or vote to enter into any contract, or the allowance of any claim. A veto may be overridden by a vote of two-thirds (2/3) of all the qualified members of the council. If the mayor neglects or refuses to sign any ordinance and fails to return it with his objections in writing at the next regular meeting of the governing body, it becomes law without his signature. The mayor may veto any item of any appropriation ordinance and approve the remainder thereof. The items vetoed may be passed over the veto as in other cases. The mayor does not have a vote in any matter involving the override of a veto.
W.S. 15-3-201