Dartmouth basketball players remain on schedule to vote Tuesday on whether to form the nation’s first-ever college athletes’ labor union after a National Labor Relations Board official rejected the school’s request to reopen the case.

NLRB regional director Laura Sacks denied the school’s request on Monday, saying there was no new evidence that wasn’t previously available to Dartmouth. Still pending is a request by the school to put off the vote.

Sacks ruled on Feb. 5 that Dartmouth basketball players are employees of the school, clearing the way for an election on whether they want to unionize. The vote is scheduled for Tuesday on the school’s Hanover, New Hampshire, campus.

All 15 members of Dartmouth’s basketball team signed the initial petition asking to be represented by the Service Employees International Union, which already includes some Dartmouth workers. One of the players, Romeo Myrthil, said last month that he had no reason to expect anything different when the players vote.

Even if the vote is in favor of a union, the the school can still appeal to the full NLRB and then to federal courts, meaning it could be years before players can negotiate a collective bargaining agreement with the school.

The outcome of the case could mean the end of the NCAA’s amateurism model, which already has begun to crumble.

The NCAA has long maintained players are “student-athletes” — a term created to emphasize that education comes first. But the NLRB ruling found that the school exerted enough control over the players’ working conditions to make them employees.

In a previous case involving the Northwestern football team, the labor relations board overturned a regional official’s similar ruling on a technicality that doesn’t apply in the Dartmouth case.