The House Judiciary Committee

Let's assume that Judge Kavanaugh is confirmed. (Not that I have any inside information on that.) If Democrats win control of the House of Representatives in November, there will surely be pressure brought to bear for the House Judiciary Committee to initiate an impeachment inquiry and, in effect, do the additional investigation that the Senate Judiciary Committee is not going to do. In that inquiry, I would assume that then-Justice Kavanaugh would be subpoenaed. There is, as far as I can tell, no precedent for a Supreme Court Justice to be subpoenaed by a congressional committee.

I wonder if he will comply when the time comes, or how that will affect the work of the Court. For example, a subpoena could be issued for a time during a Supreme Court oral argument, leaving him unable to attend. (Leave aside whether you think he would actually be impeached and put on trial in the Senate.) To what extent would an impeachment inquiry create grounds for a recusal motion in some case or another? (The Justice may need to hire outside counsel for his defense, for instance.)

UPDATE: Josh Blackman points out that Justice Clark was subpoenaed by a congressional committee looking into his conduct as Attorney General, though not for an impeachment. Clark refused to testify on separation of powers grounds, though he did offer to provide written testimony. Craig Alan Smith has an interesting paper on this in the Journal of Supreme Court History.