Representative Jerrold Nadler, the chairman of the Judiciary Committee, has claimed that the panel is already engaged in an impeachment investigation.
This has been a subject of dispute. During the Nixon and Clinton impeachment efforts, the full House voted for resolutions directing the House Judiciary Committee to open the inquiries. But it is not clear whether that step is strictly necessary, because impeachment proceedings against other officials, like a former federal judge in 1989, began at the committee level.
There are no set rules. Rather, the Senate passes a resolution first laying out trial procedures.
The Constitution clearly envisions that if the House impeaches a federal official, the next step is for the Senate to hold a trial. But there is no obvious enforcement mechanism if Senator Mitch McConnell, Republican of Kentucky and the majority leader, were to simply refuse to convene one — just as he refused to permit a confirmation hearing and vote on Mr. Obama’s nominee, Judge Merrick Garland, to fill a Supreme Court vacancy in 2016.
How the Impeachment Process Works - The New York Times