Okla. Stat. tit. 22, § 22-979: Execution of judgment by sheriff in certain cases -

Delivery to proper officer in other cases.

When the judgment is imprisonment in a county jail, or a fine,

and that the defendant be imprisoned until it be paid, the judgment

must be executed by the sheriff of the county or subdivision. In

all other cases when the sentence is imprisonment, the sheriff of

the county must deliver the defendant to the proper officer, in

execution of the judgment.