Wyo. Stat. § 41-4-311
Whenever the rights to the use of the waters of any stream and all its tributaries within the state have been adjudicated as provided by law, and it shall appear by the records of such adjudication that it had not been had at one (1) and the same proceeding, then in such case the state board of control shall be and is hereby authorized to give notice of the opening to public inspection of all proofs or evidences of appropriation of water, and the findings of the board in relation thereto from the stream and its tributaries in the manner and according to the provisions of W.S. 41-4-309; and any persons, corporations or associations who may desire to contest the claims or rights of other persons, corporations or associations, as set up in the proofs or established by the board, shall proceed in the manner provided for in W.S. 41-4-312, 41-4-313 and 41-4-314; provided, that contests may not be entered into and shall not be maintained except between appropriators who were not parties to the same adjudication proceedings in the original hearings.
W.S. 41-4-311