Kan. Stat. § 20-121
In any election held for selection of the chairman or other members of the commission to be selected by the members of the bar, in case no nominee receives a majority of the votes cast on the first ballot and two (2) or more are tied for either the first highest or the second highest number of votes cast so as to leave unsettled the determination of the question of which two (2) have received the highest number of votes, or if on either the first or second ballot two (2) nominees are tied so that one (1) additional vote cast for either would give him a majority, the canvassers shall resolve the tie by lot in such manner as they shall adopt and the winner of the lot shall be deemed to have the plurality or majority as the case may be.
K.S.A. 20-121