The board ordered a recount earlier this week after a close vote margin triggered the state's automatic recount rules.
The results showed that Stan Boehr received 3,422 votes in the race. Eugene Ulmer received 2,870 votes, while Becky Roesler received 2,852 votes. The vote margin between Ulmer and Roesler was close enough to order a recount.
Officials also say an oversight led to more than 1,000 York County voters not receiving the race on their ballot. The county election clerk sought to fix the problem by reprinting and distributing corrected ballots.
The state board decided to resolve the issue by ordering placement of all three names on the November ballot.