Graduate student at New York University are now rethinking their legal options after the school and a union scuttled a key element of their plan.

Graduate students hoping to unionize at private institutions had for years been counting on a National Labor Relations Board ruling to set a new precedent for their legal status. The decision was expected in a case involving graduate students at New York University who wished to vote to form a union affiliated with the United Auto Workers. If the board ruled in favor of the students, it could have effectively reversed a 2004 ruling that said graduate student teaching assistants at private universities did not have a right to collective bargaining.

But graduate students organizers are now regrouping after a surprise announcement from NYU and the United Auto Workers late last month: That they would withdraw their case from the NLRB, and work together to allow graduate student teaching assistants to hold a union vote mediated by the American Arbitration Association.

Having hoped to point to an NLRB decision identifying graduate students as “employees” with collective bargaining rights instead of primarily as students, organizers at other campuses are digesting the development — and appetites for a similar deal are still unclear. Meanwhile, labor experts praised the deal as a model for other campuses.

“This decision definitely changes the terrain for us,” said Molly Cunningham, a graduate student in anthropology and student organizer at the University of Chicago. That campus, known for its relatively large graduate population, has a strong, independent — but still formally unrecognized — union. Graduate Students United has achieved gains since it was formed in 2007, including doubling per-quarter pay for teaching assistants, to $3,000. But legally speaking, it has no collective bargaining power — something an NLRB decision in favor of NYU students, if it had been followed by a vote to join the union, could have changed.

The union’s course to recognition is a lot more “open-ended” now that that decision isn’t coming, Cunningham said. “[We] have a lot of collective decision-making processes to work through as we work out the implications.”

A spokesman for Chicago said the university had no comment on whether or not it would consider a deal such as NYU’s.

Graduate students at Yale University involved in the union drive there also were looking to the NYU case for recognition of their legal status. The Graduate Employees and Students Organization, affiliated with the UNITE HERE International union and the Federation of University Employees, was founded in 1991 and has sought legal recognition since.