Okla. Stat. tit. 51, § 12.1

If any officer of the state, district, county, city, town or other governmental subdivision of this state shall die while in office, and shall leave a surviving spouse, the said surviving spouse shall be eligible (if otherwise qualified) to be appointed to and to hold said office during the term for which the said officer was elected or appointed, regardless of the degree of relationship by either affinity or consanguinity to the appointing officer or to any member of the appointing board, commission, or other appointing authority, and it shall not be unlawful for any officer, board, commission, appointing authority, or member thereof to appoint or vote for the appointment of said surviving spouse to said office during said term, regardless of any such relationship.