On May 11, 2017, the Congressional Research Service released Special Counsels, Independent Counsels, and Special Prosecutors: Investigations of the Executive Branch by the Executive Branch. From the introduction:
Under constitutional principles and authorities, Congress has no direct role in federal law enforcement and is limited in its ability to initiate appointments of any prosecutor for any particular matter in which there may be allegations or concerns about wrongdoing by public officials. Instead, criminal investigations and prosecutions have generally been viewed as a core executive function and are a responsibility of the Executive Branch. However, because of the potential conflicts of interest that may arise when the Executive Branch investigates itself, as a historical matter there have often been calls for an independently led inquiry to determine whether executive officials have violated criminal law. In the past, Congress has authorized independent counsels, who were requested by the Attorney General and appointed by a judicial panel, but that authority lapsed in 1999. Currently, the Attorney General has regulatory authority to appoint a special counsel to investigate allegations that may present a conflict of interest for the Department of Justice (DOJ).
Focusing on the role of Congress, see also, Independent Counsels, Special Prosecutors, Special Counsels, and the Role of Congress (June 20, 2013, R43112). This report provides information on the procedure for the appointment of an “independent counsel,” a “special prosecutor,” or a “special counsel” to investigate and prosecute potential or possible violations of federal criminal law by officials in the executive branch of the federal government and in federal agencies. Specifically examined is the role or authority of Congress in requiring an independent or special counsel investigation of executive branch officials.