On November 15, the Wyoming Secretary of State released the official election returns. See them here. Libertarian State House nominee Bethany Baldes, in the 55th district, polled 49.2% of the vote in a two-person race. The Republican incumbent, David Miller, won with 50.8%.
Wyoming has not elected any third party nominee to the legislature since 1900, when a Populist won a State Senate seat.
Wyoming did elect an independent to the State House, in the 22nd district. This is the first time an independent had been elected to the Wyoming state house since 1976. Here is a story about Jim Roscoe, who is a former Democrat.