The U.S. attorney's office in the District of Columbia has opened a criminal investigation into Jerome H. Powell, the Federal Reserve chair, over the central bank's renovation of its Washington headquarters and whether Mr. Powell lied to Congress about the scope of the project, according to officials briefed on the situation. The inquiry, which includes an analysis of Mr. Powell's public statements and an examination of spending records, was approved in November by Jeanine Pirro, a longtime ally of President Trump who was appointed to run the office last year, the officials said.