See Full Constitution
Part Second
Article 61. Vacancies, How Filled, if No Choice
And the person having a plurality of votes in any county, shall be considered as duly elected a councilor: But if no person shall have a plurality of votes in any county, the senate and house of representatives shall take the names of the two persons who have the highest number of votes in each county, and not elected, and out of those two shall elect by joint ballot, the councilor wanted for such county, and the qualifications for councilors shall be the same as for senator.