Wyo. Stat. § 36-1-105
Whenever, in the judgment of a majority of the members of the board, the interests of the state will be advanced by granting, conveying or deeding to the United States of America, any lands which have been heretofore granted, selected by, and patented to the state, then, in such case said board is hereby authorized and empowered to so grant, convey and deed to the United States of America, such lands. And the president of said board, and the director are authorized and empowered to execute and deliver all necessary instruments to complete such grant, or conveyance; provided, always, that no such lands shall be so granted, conveyed and deeded, unless the United States of America shall, and will permit and allow this state to select, and have patented to it, other lands in lieu of the lands so reconveyed to the United States of America subject to W.S. 36-1-111; provided, however, that the state shall not give both surface and mineral rights with any lands exchanged unless it receives the same from the federal government.
W.S. 36-1-105