Mont. Code Ann. § 5-15-104

A vacancy on the committee occurring when the legislature is not in session shall be filled by the selection of a legislator by the remaining members of the committee. If there is a vacancy on the committee at the beginning of a legislative session because a member's term of office as a legislator has ended, a member of the same political party must be appointed in the same manner as the original appointment, no later than the 10th legislative day, to serve until a successor is appointed under 5-15-101.