The Columbia students have asked the labor board’s New York office to oversee a unionization election, but it has refused, citing the 2004 ruling. The students hope to persuade the agency’s five-person board in Washington to reverse the 2004 ruling, which was decided by an employer-friendly, Republican-dominated board. Today’s board has a Democratic majority and is friendlier to labor.

“Given the success at N.Y.U. and some positive signals from the N.L.R.B., students at numerous schools are eager right now to pursue unionization,” said Ruth Milkman, a labor expert at the City University of New York. “There’s good reason to think the N.L.R.B. will rule their way.”

Columbia officials say the school is generous to teaching and research assistants, paying full tuition and stipends. Students say they receive $22,000 to $40,000, varying by department. Like many universities, Columbia fears that a union could bring tensions and strikes.

“We fully understand that pursuing a Ph.D. is a highly challenging path, both intellectually and personally,” Columbia said in a statement. “Our graduate students are scholars in training whose teaching and research are an integral part of their doctoral studies. As the N.L.R.B. found in the Brown University case, we believe that treating students as employees could adversely affect their educational experience.”

Seth Prins, a Ph.D. candidate in epidemiology, asserted that it was wrong for Columbia and the labor board to consider the teaching and research assistants merely students. “If we stopped providing our teaching and research services to the university, it would cease to be the world-class institution it is,” he said. “Being a student is not incompatible with being a worker.”

The Columbia students are seeking to join the United Automobile Workers, which represents thousands of white-collar workers, including Columbia’s clerical workers, as well as N.Y.U. and University of Connecticut graduate students.

Alex Beecher, a fourth-year Ph.D. student in chemistry, has reservations about unionizing.

“I’m happy with the current situation,” he said. “We get a fair package from Columbia.”