Kan. Stat. § 19-504
In case the office of county treasurer shall become vacant, there shall be appointed a successor to perform the duties of such treasurer, and the person so appointed, upon giving bond, with the like sureties and conditions as that required in county treasurer's bonds, and in such sum as the board of county commissioners shall direct, shall be invested with all the duties of such treasurer. If the vacancy occurs on or after May 1 of the second year of the term, the person so appointed shall serve for the remainder of the unexpired term and until a successor is elected and qualifies. If the vacancy occurs before May 1 of the second year of the term, the person appointed to fill the vacancy shall serve until a successor is elected and qualifies at the next general election to serve the remainder of the unexpired term. Nomination and election of such successor shall be in the same manner as nomination and election of a county treasurer for a regular term. Appointments hereunder shall be made in the manner provided by law for filling vacancies in the office of member of the house of representatives.
K.S.A. 19-504