Arlington Superintendent Charles E. Nunley has requested a fiscal 1984 school budget requiring a 7.2 percent increase in local funds to $52 million, about $2 million more than the 4.5 percent increase county officials proposed last fall before Democrats regained a majority on the County Board.

Nunley made his recommendation last night when he gave the School Board three budget plans, all of them including 4 percent salary increases for school employes. Nunley called the $50.7 million budget proposed under the Republican majority a "bare bones budget" that would require cutting 58 staff positions, at least 15 of them teaching jobs.

"These reductions are considered drastic and would have a very negative effect on the instructional program . . . ," Nunley said. "I cannot support educationally the cuts to meet that."

School Board Chairman Evelyn Reid Syphax suggested that the board not consider the $50.7 million proposal, but received no support from her colleagues. "I didn't want to waste time looking at something we weren't going to vote," she said.

Depending on which plan is approved, total spending--including a projected $14 million in state and federal aid--could rise 8.5 percent from the current $62 million to as high as $67.3 million.

School officials will approve a final budget request Feb. 24, but the County Board, which funds more than 75 percent of the school budget, will determine the final amount. In September, County Manager Larry J. Brown, hired by the former Republican-controlled board, proposed increasing local funding from the current $48.5 million to $50.7 million.

The Nunley budget recommendation may be one of the first tests of the new Democratic majority, whose members have expressed concern that the Republican board too often "sacrificed excellence to small economies," as Democratic Board Member Mary Margaret Whipple put it.

When asked if his budget request was shaped by the attitude of the new board, Nunley said, "You're not going to get me in that discussion."

Nunley's middle range budget, a 6.5 percent budget increase to $51.7 million, would require cutting 31 positions, mostly aides and secretaries, but would otherwise maintain the current operating level, he said.

Funding at the $52.7 million recommendation would require few dismissals and allow for additional text books, library materials, vocational equipment, three new teachers for foreign-speaking students and $300,000 for capital improvements, he said.