Cheney has been one two anti-Trump Republicans who was chosen by House Speaker House Nancy Pelosi (D-CA) to be a member of the committee. She said:
The committee has approved recommending some ex-Trump officials be held in contempt of Congress, and the entire U.S. House has voted to refer instances of contempt which led to the prosecution of officials in defiance of DOJ's policy not referring cases of contempt.
Democrats and many in the media mainstream have been pushing the committee to present an argument for the DOJ to file accusations against Trump and his advisors. The absence of a criminal referral does necessarily mean the DOJ will not investigate Trump or his associates. The DOJ has made use of transcripts of committee's depositions in closed-doors during an investigation into criminal conduct.
The conflict between Thompson and Cheney proves is a sign there are two voices that are not in harmony within the committee.