Wyo. Stat. § 41-9-260
In all cases where the work to be done at any one time under the direction of the commissioners shall, in their opinion, cost to exceed five hundred dollars ($500.00), the same shall be let to the lowest responsible bidder, and the commissioner shall advertise for sealed bids, by notice published in some newspaper published in the county in which the petition is filed, and may advertise in one (1) or more newspapers published elsewhere. If there be no newspaper published in the county in which the petition is filed, they shall advertise in some newspaper published in an adjoining county, which said notice shall particularly set forth the time and place when and where the bids advertised will be opened, the kind of work to be let and the terms of payment. Said commissioners may continue the letting from time to time, if in their judgment the same shall be necessary, and shall reserve the right to reject any and all bids.
W.S. 41-9-260