Okla. Stat. tit. 22 § 1358
If the Executive Director determines that a conflict exists after evaluating a case assigned pursuant to Section 1356 of this title, the Executive Director shall reassign the case in the same manner as is provided for conflicts at the trial level in Section 1355.7 of this title, unless the case is from a county subject to the provisions of Section 138.1a of Title 19 of the Oklahoma Statutes and the indigent defendant was not represented at trial by the county indigent defender. If the Executive Director determines a conflict exists in a case from a county subject to the provisions of Section 138.1a of Title 19 of the Oklahoma Statutes and the indigent defendant was not represented at trial by the county indigent defender, the county indigent defender shall be appointed to represent the indigent defendant. The appointment of the county indigent defender shall be made by the district court at the time the appeal is initiated or by the Court of Criminal Appeals after the appeal is initiated. If the district court, at the time the appeal is initiated, or the Court of Criminal Appeals, after the appeal has been initiated, determines that the county indigent defender also has a conflict of interest in the case, the district court, initially or on remand from the Court of Criminal Appeals, shall appoint counsel in the same manner as is provided for conflicts at the trial level in Section 138.7 of Title 19 of the Oklahoma Statutes, by reassigning the case to another county indigent defender, an attorney who represents indigents pursuant to contract, or a private attorney has agreed to accept such appointments.
Okla. Stat. tit. 22, § 1358