During the interview with committee aides, Mr. Uthmeier said he had consulted John S. Baker, a visiting professor at Georgetown Law and a longtime mentor of his, “to obtain information on how citizenship data was used historically.”

Lawyers for the Commerce Department, which oversees the Census Bureau, blocked Mr. Uthmeier from answering nearly 100 questions during the session, including what Commerce Secretary Wilbur Ross told him were his reasons for trying to add a citizenship question.

A spokesman for the department defended Mr. Uthmeier’s testimony on Tuesday in a statement, saying that the lawyer answered more than 400 questions and that his decision to decline to discuss privileged communications was “entirely appropriate.”

The release of the documents is the latest episode in a politically charged battle over the committee’s attempts to investigate the Trump administration’s decision to ask 2020 census respondents whether they are citizens. The Oversight Committee voted largely along party lines this month to recommend that Mr. Ross and Attorney General William P. Barr be held in contempt of Congress, after President Trump invoked executive privilege to block the disclosure of documents on the decision. Representative Justin Amash of Michigan was the only Republican to vote for the recommendation.

The issue is currently before the Supreme Court, which is expected to decide the legality of the question within weeks. Conservatives backing the addition of the question have said it is reasonable to know how many residents are citizens, and the Justice Department has argued that Democrats’ allegations are “smoke and mirrors.”