Hillary Rodham Clinton was directly asked by congressional investigators in a December 2012 letter whether she had used a private email account while serving as secretary of state, according to letters obtained by The New York Times.

But Mrs. Clinton did not reply to the letter. And when the State Department answered in March 2013, nearly two months after she left office, it ignored the question and provided no response.

The query was posed to Mrs. Clinton in a Dec. 13, 2012, letter from Representative Darrell Issa, the Republican chairman of the House Committee on Oversight and Government Reform. Mr. Issa was leading an investigation into how the Obama administration handled its officials’ use of personal email.