The vote to convict a guilty official is more commonly known as the impeachment process. Impeachment can be done if the officials are proven to leverage their status to be involved in Treason, Bribery, or other high Crimes and Misdemeanors.
The impeachment is started by the House of Representative, but the Senates were the one that made the vote for the convict. The senates all 50 states in USA. The officials will be impeached if 67 out of 100 senates voted for it.