Okla. Stat. tit. 19, § 547.1

Assigned duties outside county of employment - Powers and duties of officers. Any Oklahoma sheriff, deputy sheriff, or a reserve deputy sheriff who is assigned to perform duties outside of his or her county of employment shall have the same powers and duties as though employed by the sheriff’s office for which he or she is performing duties. Liability for the conduct of any sheriff, deputy sheriff, or reserve deputy sheriff, while performing duties outside of his or her county of employment, shall remain the responsibility of the county in which he or she is regularly employed. Salaries, insurance, and other benefits shall be provided in the regular manner by the county in which the sheriff, deputy sheriff, or reserve deputy sheriff is regularly employed.