“The indictment or criminal prosecution of a sitting President would unconstitutionally undermine the capacity of the executive branch to perform its constitutionally assigned functions.” -- DOJ opinion, October 16, 2000
The Department of Justice has long held that it would be unconstitutional to criminally charge and prosecute a sitting president. The Constitution itself expressly states that “indictment, trial, judgment and punishment” can occur only after a president is convicted upon impeachment (Article 1, Section 3).
However, there is nothing to prevent a special counsel from investigating a president and leveling an accusation with no formal charge. The accusation could be completely manufactured and meritless. Proving it in a court of law would be irrelevant because impeachment is a political act, not a legal one.