WASHINGTON — A federal judge on Tuesday heard final arguments in a case brought by Charles M. Kupperman, President Trump’s former deputy national security adviser, who asked for clarity from a federal court about whether he must testify to Congress amid a constitutional clash between House investigators and the White House.

During the impeachment inquiry into Mr. Trump, Mr. Kupperman’s case became a highly anticipated test of the extent of congressional oversight, and the power House Democrats have to compel senior-level White House officials to testify despite Mr. Trump’s orders not to. The decision in Mr. Kupperman’s case was expected to have implications for other witnesses House Democrats had hoped to call, such as John R. Bolton, the former national security adviser.

But as House Democrats have raced ahead, unveiling articles of impeachment on Tuesday, they lost interest in litigating Mr. Kupperman’s case and asked the judge to dismiss it, leaving open the question of what relevance to the proceedings any decision may now have, or whether there is even still a dispute to settle.

Mr. Kupperman maintains that there is. He was subpoenaed on Oct. 25 by House Democrats, but did not show up to testify after the president invoked “constitutional immunity,” directing aides to ignore congressional subpoenas. On the same day as the subpoena, Mr. Kupperman’s lawyers filed a lawsuit asking a judge to settle the question of whether the executive branch could order him to ignore the demands placed upon him by Congress.