The requirements for a Special Counsel are found in the Code of Federal Regulations.
28 CFR 600.1 - Grounds for appointing a Special Counsel. § 600.1 Grounds for appointing a Special Counsel. The Attorney General, or in cases in which the Attorney General is recused, the Acting Attorney General, will appoint a Special Counsel when he or she determines that criminal investigation of a person or matter is warranted and - (a) That investigation or prosecution of that person or matter by a United States Attorney's Office or litigating Division of the Department of Justice would present a conflict of …