Okla. Stat. tit. 22, § 1356

A. The System shall perfect all direct appeals and capital post-conviction proceedings for all cases to which the System is appointed by Oklahoma district courts at the time the appeal is initiated, except as otherwise provided in this section and Section 1358 of this title. In counties subject to the provisions of Section 138.1a of Title 19 of the Oklahoma Statutes, the System shall perfect direct appeals for indigent defendants who were not represented at trial by the county indigent defender. The System shall not be appointed to perfect direct appeals for indigents represented at trial by the county indigent defender, unless a conflict of interest on appeal exists between defendants, in which case the System may be appointed to represent not more than one defendant. B. Judges of the district courts shall appoint the System, at the time the appeal is initiated, in cases in which the defendant is subject to incarceration or the death penalty, and to perfect all indigent criminal appeals which are felony or misdemeanor appeals, appeals by petition for writ of certiorari, juvenile criminal appeals and youthful offender appeals pursuant to the Oklahoma Juvenile Code, appeals from revocation of a suspended sentence and appeals from acceleration of deferred judgments.