What is the term used for the formal accusation of misconduct against a public official?

The term that the definition refers to is impeachment. Impeachment is usually done by a legislative body, who will charge an elected government official with a crime. When someone is impeached, the legislative body of the government would run a vote that would determine whether the individual would be removed from office or not.

Some recent cases where head of governments were impeached in their country, was in South Korea, where former President Park Geun-hye was impeached and imprisoned for 24 years due to influence peddling; and in Brazil, where former President Dilma Roussef was impeached due to administrative misconduct and disregard of federal budget.