At issue in the House race were seven ballots that had ovals filled in for both Mr. Cross and Mr. Jore. Election officials awarded those ballots to Mr. Jore, as did a recount board.
Ms. Windham, a businesswoman, appealed to District Court in Lake County. Judge Kim Christopher upheld the decision of the recount board, arguing that otherwise the race would go to Ms. Windham, for whom none of the disputed ballots were cast.
After Governor Martz broke the tie by appointing Mr. Jore to the seat, Ms. Windham appealed to the Montana Supreme Court, and the seven contested ballots were driven to the court by a state Highway Patrol officer.
In its brief order, the Supreme Court declared "one or more" of the contested ballots invalid, a move that broke the tie in favor of Ms. Windham.
"I'm disappointed," said Mr. Jore, a businessman in Charlo. "I felt the ballots in question were clear." He added, "They obviously intended to vote for me." Mr. Jore said three of the voters whose ballots were in question called him and said they had intended to vote for him.
Mike Meloy, a lawyer for Anita Big Spring, a voter who brought the case to the Supreme Court, said the decision was the right one. "There is no way for anybody to tell from those ballots what the voter intended," Mr. Meloy said. "Those voters violated the instructions given them, which was don't change your ballot and if you make a mistake, ask for a new ballot. Why would you want to give special consideration to someone who didn't follow instructions?"