Mont. Code Ann. § 5-12-204

If a vacancy occurs on the committee when the legislature is not in session, the remaining members shall select a member of the appropriate political party and appropriate committee, as provided in 5-12-202, to complete the unexpired term. 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 5-12-202.