Supreme Court justices can be impeached and the procedure is the same as impeaching the president--the House impeaches and the Senate holds a trial. The reference of course is The Constitution:
Article III
Section 1.
The judicial power of the United States, shall be vested in one Supreme Court, and in such inferior courts as the Congress may from time to time ordain and establish. The judges, both of the supreme and inferior courts, shall hold their offices during good behaviour, and shall, at stated times, receive for their services, a compensation, which shall not be diminished during their continuance in office.
'Good behaviour' is not defined, but Art. II Sec.4 specifies: 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.
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