Mark Chilton became mayor in December, leaving his alderman seat empty with two years left in his term.
The board appointed Dan Coleman to the seat in February. He was one of 12 people who had applied for it.
Some thought the town's charter required giving the seat to the fourth-highest vote getter in the November election, who last fall was Katrina Ryan.
But Town Attorney Mike Brough said that would have been the case only if the vacancy had occurred before the election. Because Chilton's seat did not become vacant until afterward, the aldermen had the authority to appoint someone.