ORS § 34.355
If counsel is appointed by a court to represent, in an initial proceeding by habeas corpus or on appeal as provided in ORS 34.710, a person who is imprisoned or otherwise restrained of liberty by virtue of a charge or conviction of crime and who is determined to be financially eligible for appointed counsel at state expense, the executive director of the Oregon Public Defense Commission shall determine compensation for counsel and costs and expenses of the person in the proceeding or on appeal. Compensation for counsel and expenses of the person in an initial proceeding or in a circuit court on appeal shall be determined and paid as provided in ORS 135.055. Compensation for counsel and costs and expenses of the person on appeal to the Court of Appeals or on review by the Supreme Court shall be determined and paid as provided in ORS 138.500. The compensation and expenses so allowed in an initial proceeding in a county court shall be paid by the county in which the person was charged or convicted of crime.
ORS 34.355