Later this week, a resolution on investigating President Donald Trump will be brought before the House of Representatives for a vote, turning the semi-official process officially official.
House Speaker Nancy Pelosi (D–Calif.) sent out a "Dear Colleague" letter today (that also functions as a press release), stating that the resolution formalizing the inquiry is moving forward:
This week, we will bring a resolution to the Floor that affirms the ongoing, existing investigation that is currently being conducted by our committees as part of this impeachment inquiry, including all requests for documents, subpoenas for records and testimony, and any other investigative steps previously taken or to be taken as part of this investigation.
This resolution establishes the procedure for hearings that are open to the American people, authorizes the disclosure of deposition transcripts, outlines procedures to transfer evidence to the Judiciary Committee as it considers potential articles of impeachment, and sets forth due process rights for the President and his Counsel.
The letter somewhat testily observes that Trump, White House staff and counsel, and allied Republicans are not treating the ongoing inquiry and investigation as though it's legitimate because the House hasn't voted on it. Pelosi makes it clear that such a vote is not required, and previous impeachment inquiries often have not had such votes. But nevertheless, because the House is having a hard time getting witnesses to cooperate (just this morning, former Deputy National Security Adviser Charles Kupperman blew off a congressional subpoena and did not appear as ordered), Pelosi says the House will make it official.
Pelosi includes the short summary of the resolution in the letter: "Directing certain committees to continue their ongoing investigations as part of the existing House of Representatives inquiry into whether sufficient grounds exist for the House of Representatives to exercise its Constitutional power to impeach Donald John Trump, President of the United States of America, and for other purposes."
To be very clear, this is not a vote to impeach Trump. It is a vote to formalize that Trump is being investigated for possible impeachment. If the House eventually votes to impeach Trump (which seems increasingly likely), it will be the Republican-controlled Senate who holds the impeachment trial. It would take a two-thirds vote in the Senate to remove Trump.