The boards of county commissioners of the two counties, participating in a joint ferry, shall meet in joint session at the county seat of one of the counties interested, and shall elect one of their members as chair of the joint board of commissioners, who shall act as such chair during the remainder of his or her term of office, and, at the expiration of his or her term of office, the two boards of county commissioners shall meet and elect a new chair, who shall act as such chair during his or her term of office as county commissioner, and they shall continue to elect a chair in like manner thereafter. The county auditors of the counties shall be clerks of such joint commission, and the county auditor of the county where each meeting is held shall act as clerk of the commission at all meetings held in his or her county. Each county auditor, as soon as the joint commission is organized, shall procure a record book and enter therein a complete record of the proceedings of the commission, and immediately after each adjournment the county auditor of the county in which the meeting is held shall forward a complete copy of the minutes of the proceedings of the commission to the auditor of the other county to be entered by him or her in his or her record. Each county shall keep a complete record of the proceedings of the commission.