Okla. Stat. tit. 12, § 12-990.5
Stay of enforcement against political subdivisions of
the state.
Notwithstanding any other provision of this title, the execution
of a judgment or final order of any judicial tribunal against any
county, municipality, or other political subdivision of this state
is automatically stayed without the execution of supersedeas bond
until any appeal of such judgment or final order has finally been
determined.