§ 26 O.S. § 26-12-111Vacancies in county elective offices

A. Whenever a vacancy shall occur in the office of a county
commissioner, the vacancy shall be filled at a special election to
be called by the Governor within thirty (30) days after the vacancy
occurs. Provided, no special election shall be called if the
vacancy occurs in an even-numbered year if the term of the office
expires the following year. In such case, the candidate elected to
the office at the Primary Election, runoff Primary Election, or the
regular General Election shall be appointed by the Governor as soon
as practical after the applicable election to fill the unexpired
term.
B. Whenever a vacancy shall occur in any elective county office
of any county in this state having a population of more than the
population figure specified in subsection B of Section 10 of Title
51 of the Oklahoma Statutes, the vacancy shall be filled at a
special election to be called by the Governor within thirty (30)
days after the vacancy occurs. Provided, no special election shall
be called if the vacancy occurs in an even-numbered year if the term
of the office expires the following year. In such case, the
candidate elected to the office at the Primary Election, runoff
Primary Election, or the regular General Election shall be appointed
by the Governor as soon as practical after the applicable election
to fill the unexpired term.