This week, Mr. Trump’s White House counsel, Pat A. Cipollone, sent a letter to the House declaring that the administration would not cooperate with the House’s impeachment inquiry, such as by providing documents or permitting witnesses to testify.

The Trump legal team has separately argued that Mr. Trump’s current and former White House aides are absolutely immune from subpoenas for their testimony — meaning they would not even have to show up — and that Congress lacks legitimate legislative authority to scrutinize potential wrongdoing in the executive branch.

The appeals court ruling on Friday centered on that third argument, and it was in some respects already obsolete because the premise of the argument was that the House was relying only on its routine legislative and oversight authorities, rather than any extra investigative powers that lawmakers gain when engaged in an impeachment inquiry.

But since the Mazars case started going through the courts, the House Judiciary Committee and Speaker Nancy Pelosi have declared that the chamber is conducting an impeachment inquiry. The Trump administration has disputed that premise, since the full House has not voted for a resolution approving such an investigation.

Friday’s ruling did not address the question of whether an impeachment inquiry is underway — and, if so, whether that matters. The majority on the panel ruled for the House without any need to invoke its impeachment powers.

Specifically, the fight centered on whether the House Oversight and Reform Committee had the authority to compel Mazars to turn over Mr. Trump’s financial records as part of its routine legislative and oversight powers, even if the committee’s purpose was in part to determine whether Mr. Trump committed crimes.

The committee, led by Mr. Cummings, issued the subpoena after it came to light that Mr. Trump had failed to list on his ethics disclosure forms a debt that he owed and then repaid to his former lawyer and fixer, Michael D. Cohen, for paying hush money to a pornographic actress just before the 2016 election to keep quiet about an affair she claimed to have had with Mr. Trump. He has denied the relationship.