The House of Representatives shall chuse their Speaker and other Officers; and shall have the sole Power of Impeachment.
Senate:
The Senate shall have the sole Power to try all Impeachments. When sitting for that Purpose, they shall be on Oath or Affirmation. When the President of the United States is tried, the Chief Justice shall preside: And no Person shall be convicted without the Concurrence of two thirds of the Members present.
Congress:
The President, Vice President and all Civil Officers of the United States, shall be removed from Office on Impeachment for, and Conviction of, Treason, Bribery, or other high Crimes and Misdemeanors.
It seems as if the House can impeach for any reason, with the only requirements being one of votes and at least claiming the offense is Treason, Bribery, or other high Crimes and Misdemeanors.
The Senate is also pretty much free, beyond the two thirds requirement.
No court can review these actions and so there is no case law or precedent. Sure, people can say, "They didn't do it this way last time". But so what? No court can overturn such decisions.
Added: Many Democrats and some "Republicans" are saying that impeachment is like an indictment and so the Senate is required to conduct a trial with witnesses called. As above, the Senate has sole power to try and can set whatever rules they choose. But also, many Democrats crowed that Trump's presidency will forever be stained by impeachment. In criminal and civil law, there is no stain attached to your name or conduct if you are found non-guilty. So there is a little bit of having your cake and eating it too with all this.
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