WASHINGTON — When Chief Justice John G. Roberts Jr. walks out of his chambers at the Supreme Court, crosses First Street and enters the Capitol to preside over President Trump’s impeachment trial, he will leave behind an institution that prides itself on reason and decorum and enter one marked by partisan warfare.

The chief justice’s responsibilities at the trial are fluid and ill-defined, and they will probably turn out to be largely ceremonial. What is certain is that they will be full of peril for his reputation and that of his court.

“It’s not a heavy lift, but it’s going to put him in a very, very unpleasant role,” said Philip Bobbitt, a law professor at Columbia and an author, with Charles L. Black Jr., of “Impeachment: A Handbook.” “I’m sure he’ll get ulcers.”

That role could begin as early as Thursday when, after a monthlong delay, the House will vote to appoint a team of lawmakers, known as managers, to prosecute the case against Mr. Trump and, in a highly choreographed exchange, transmit the articles to the Senate.