Ms. Miller said that both candidates had five days to file a legal challenge to the results. And if the court decided the recount went as it should have, and the race was still a tie?

The prevailing candidate would be determined “by lot,” Ms. Miller said. “It could be a coin toss or some other way of deciding, as long as it’s random.”

It would not be the first time an Alaska race was determined by coin toss.

In 2006, State Representative Bryce Edgmon, a Democrat from Dillingham, beat the incumbent, Carl Moses. Mr. Moses’s name was drawn, so he got to make the call: Heads.

The state’s elections director at the time flipped an Alaska Mint medallion — the side with a walrus being heads and the side with the state seal being tails. It landed state seal side up.

Ms. Miller would not speculate about when the recount would be complete, but said both candidates were present, along with observers and officials.

Mr. LeBon did not respond to requests for comment on Friday.

Sara Harriger, a spokeswoman for Ms. Dodge, said in a statement that during Friday’s recount, one additional vote was found for Ms. Dodge and a challenged ballot was allowed for her opponent, Mr. LeBon, which meant that the tally stood at 2,662 apiece. Still tied.

Ms. Dodge said in a statement that she believed every legally cast ballot should be counted. “I just want everyone watching this process to take away a sense of confidence in our democratic system and a commitment to cast their votes in future races,” she said, “and knowing that their votes will matter.”