The D.C. school board will defy the Barry administration's order to propose cuts in school spending as part of a possible $28 million municipal belt-tightening, the board president said yesterday.

R. Calvin Lockridge, who was elected to the board's top job just two weeks ago, said a majority of the 11 board members agree they should not act on the directive by City Administrator Elijah B. Rogers that school officials seek ways to cut the current school budget by nearly $8.4 million.

"It is my feeling that the city administrator cannot direct the school board to entertain any cuts," Lockridge declared.

In a letter hand-carried last night to the mayor's office, Lockridge offered to meet with the mayor to discuss the issues.

As a result of budget cuts already made by the city and Congress, Lockridge wrote, the school system "may well be unable to make the necessary large-scale purchases of textbooks and equipment for next school year, and also may be unable to maintain buildings at projected levels." The cuts also threaten court-mandated tuition grants for special education, he said.

Unlike most city agencies, the school board enjoys statutory autonomy in spending its money once the city's annual budget is appropriated by Congress. This independence was reinforced in 1978 by a D.C. Superior Court ruling that the mayor lacked authority to withhold such funds once they are appropriated.

While the directive to city agencies to find ways to cut outlays by a total of $28 million sent shock waves through the District government, it was portrayed by top officials as a way of dealing with the worst possible case that could arise as the result of a projected shortfall in city tax collections.

Rogers and ivanhoe donaldson, general assistant to Barry, said they hope to avert a general job freeze and lay-offs -- two possibilities raised by the Rogers' directive -- and said that any such moves that might come would be imposed selectively.

D.C. budget director Gladys Mack, in a document that accompanied the Rogers' directive, set a goal for agencies to proposed cuts of $29,055,600 from the $1,384,102,900 in basic operating funds appropriated by Congress for the current fiscal year, which ends Sept. 30.

Rogers, in his directive Thursday, used a slightly lower reduction goal, $28 million, as the result of a refinement in revenue projections, a budget official said.

Among the propopsed departmental reductions are $3.9 million from human resources, $1.9 million from environmental services, $4.1 million from the police, $1.4 million from the fire department and $1.5 million from corrections. The mayor's office would take a cut of $33,600 and the City Council, $119,000.

Many department heads were closeted with their budget officers seeking to meet the Monday deadline set by Rogers for submitting their reports.

The director of the city's largest agency, Albert P. Russo of the Human Resources Department, said that meeting the cutback goal would bring "traumatic and harsh measures in the personnel area" -- the probable abolition of overtime and a hiring freeze on jobs paid with city (but not federal) funds.

Barry, talking with reporters, would not comment in detail on the possible cutback. He said he supported Rogers, saying the administrator "has identified the situation early enough to get on top of it."

Rogers, calling his directive "a manaagement tool," said the suggested $28 million cutback was based on the possibility of a worst possible situation.

"If we continue to spend at the same rate and no other revenue comes in, we would be $28 million in the red [on Sept. 30] and the law says we can't do that," he said in an interview.

Carolyn Smith, Barry's nominee as director of the Finance and Revenue Department, told a council hearing on her confirmation that current signs show an approaching downturn in tax revenues. Smith, now acting as departmental director, said the figures will be rechecked next month.

Rogers said the city is expected to submit a supplemental request to Congress later this year that could include all or part of the $62 million remaining for the authorized 1980 federal payment.

But a spokesman for Sen. Patrick J. Leahy (D-Vt.), chairman of the D.C. appropriations subcommittee, said the city cannot expect Congress "to bail it [the city] out" from the $28 million shortfall.

Donaldson, the mayoral assistant, said that if reductions are needed they would be done selectively on a case-by-case basis. Actual layoffs would be the least desirable alternative, he said.

Rogers said the expected shortfall resulted partly from paying off loans the city took in past years. "If we don't get an increased . . . federal payment and if we don't reduce our expenditures, we will . . . end up looking like New York City."