Secretary of Health, Education and Welfare Joseph A. Califano Jr., already in trouble in tobacco-growing North Carolina for denouncing smoking, may be headed for more difficulties there over desegregation of the state university system.

Last May 12, Califano and North Carolina officials announced a plan to desegregate the system and avert a cutoff of $89 million to $100 million in HEW funds for it.

Part of the plan involved a promise by the state to examine situations in which a formerly all-black college and a nearby formerly all-white one each had a similar special curriculum in engineering or some advanced progam in another subject.

Such duplication, it was argued, encouraged white students to continue applying only to the white institution, leading in effect to a continuation of the colleges as overwhelmingly white and overwhelmingly black. By ending duplication -- for example, putting all Master of Arts courses in one subject into one of the black colleges, so that white students desiring that program would have to go there -- the state could hasten desegregation. The state in the May 12 agreement promised to come up with a Five-year plan to end all educationally unnecessary duplication.

On Dec. 11, the state sent HEW reports on the duplication issue and although they listed about 57 major sets of duplications, they concluded that none was educationally unnecessary and therefore none would be ended.

Yesterday Joseph L. Rauh, attorney for a group of students and the NAACP Legal Defense Fund in a lawsuit which led to the formulation of the desegregation plan, wrote Califano that the North Carolina plan is "massive resistance to desegregation of higher education."

The North Carolina position, he said, amounted to "nullification" and made it necessary for HEW to stop negotiating with the state and start moving toward a cutoff of federal funds.

A Rauh partner, Elliott Lichtman, said Rauh would go back to court to achieve this end unless Califano took strong steps to force North Carolina to move on duplication.

"We're urging Califano to stand by his own criteria so we won't have to go to court," he said.

Rauh's letter quoted Dr. Kenneth Clark, the sociologist, as saying the North Carolina position amounted to "stonewalling."

At the time of the May 12 agreement, Califano clearly indicated to reporters that he expected North Carolina would come up with some plan to end duplications. Unless a compromise is reached, Califano could move to cut off funds.

HEW spokesmen said yesterday they had no comment, that the agency is still studying the state reports.

The North Carolina desegregation case involves 16 units of the state university system. They are the University of North Carolina at Chapel Hill, North Carolina State at Raleigh, Pembroke State, West Carolina, East Carolina, Appalachian State, the North Carolina School of the Arts, the State University at Greensboro, the State University at Charlotte, the State University at Asheville, and the State University at Wilmington, along with five traditionally all-black schools: North Carolina A&T at Greensboro, Winston-Salem State, North Carolina Central, Elizabeth City State and Fayetteville State.