But what happens if the president is convicted by the Senate? Here’s the constitutional answer:
Judgment in Cases of Impeachment shall not extend further than to removal from office, and disqualification to hold and enjoy any Office of honor, Trust or Profit under the United States: but the Party convicted shall nevertheless be liable and subject to Indictment, Trial, Judgment and Punishment, according to Law.
A reasonable interpretation of this provision is that it sets out a temporal sequence: Impeachment, then conviction and removal from office -- and only after that, indictment, trial, judgment and punishment.
Alexander Hamilton
seemed to read the provision exactly that way:
“The President of the United States would be liable to be impeached, tried, and, upon conviction of treason, bribery, or other high crimes or misdemeanors, removed from office; and would afterwards be liable to prosecution and punishment in the ordinary course of law.”
That means you can’t indict and try a sitting president. He has to be removed first.
True, this interpretation isn’t inevitable. You could read the text to mean only that the consequence of conviction is removal from office, and that a convicted president can be prosecuted -- but to be silent on, and so not to resolve, the question whether a president can be prosecuted for crimes while in office. On that interpretation, nothing in the Constitution rules out a prosecution of the president for (say) obstruction of justice or for perjury.