WASHINGTON — When Brett M. Kavanaugh came before the Judiciary Committee in May 2006 for his nomination to be an appeals court judge, senators pressed him on his role in President George W. Bush’s use of signing statements to claim the power to bypass new laws — like a much-disputed assertion the previous December that he could override a ban on torture.

Judge Kavanaugh, who at the time was the White House staff secretary, acknowledged handling draft signing statements to ensure that “relevant members of the administration have provided input” before presenting them to Mr. Bush. But the nominee sidestepped questions about any advice or views he had about them, refusing to discuss “internal matters” and pivoting instead to a description of a 1952 Supreme Court opinion that explains how to analyze separation-of-powers disputes in general.

Now that President Trump has nominated Judge Kavanaugh to the Supreme Court, the opacity of his testimony about Mr. Bush’s signing statements, including about the torture ban, is becoming a case study for Democrats’ vehement arguments that the Senate must see his staff secretary files before any confirmation hearing. Democrats have already been raising concerns that Judge Kavanaugh may hold too expansive a view of executive power in other contexts, like his skepticism about the wisdom of forcing a president to answer questions in criminal investigations.

“Judge Kavanaugh played a key role in clearing President Bush’s use of signing statements,” said Senator Chuck Schumer of New York, the Democratic leader. “Understanding the nature of his involvement in those actions is absolutely critical to evaluating the type of justice he would be on the bench. The Senate and the American people deserve full access to the documents from his time as staff secretary.”