Mayor Marion Barry is a busy man, but not too busy to keep score in long-running, point-making squabble with the D.C. public school system.

He showed this penchant for political infighting yesterday by challenging an auditor's report on the schools' finances that appeared to refute his criticisms of the system.

Barry said that when he read about the auditor's report in The Washington Post yesterday, he assigned members of his staff to review it because he did not believe its most important conclusion, which was that the schools underspent their budget by $40,000 in the last fiscal year by slashing administrative and overhead costs.

By midafternoon, columns of figures at hand, he was ready to take the offensive. He telephoned a Post reporter to say he was "following all this carefully" and had concluded that school officials were "not quite candid" in their assessment of the auditor's findings.

Rather than showing that the school system sacrificed administrators to save classroom teachers, Barry said, the report actually supported his contention that the Board of Education faced with the need to reduce spending, had dismissed teachers while protecting administrators and management personnel.

"Those reductions came right out of school operations," Barry said. "And they're doing it even more this year."

Barry was unaware as he spoke yesterday that Vincent Reed, the superintendent of schools, disclosed that he is quitting his job at the end of this month. Reed attributed his decision to weariness with the constant infighting and personal antics of the school board. But he has made no secret in the past of his unhappiness at being the man in the middle of the mayor's budgetary battles with the school system. Reed has publicly accused Barry, a former school board president, of conducting a "war" against the public schools.

What set off the latest skirmish was a report submitted to the school board on Monday night by the nationally known accounting firm of Arthur Andersen & Co. School officials, who have been trying to muster public support for their budgetary requests in the face of Barry's attempts to cut back, happily passed out copies to the press because it showed that they had spent $5.7 million less than was authorized in "management services" in the fiscal year that ended Sept. 30.

That, the report showed, nearly offset $6.19 million in overspending on "school operations -- that is, teacher salaries and other classroom costs. The report appeared to vindicate the school system and to refute Barry's charges that education was being sacrificed for a top heavy bureaucracy.

Barry said yesterday that was valid only when school spending was measured against an amended budget adopted late in the school year. When compared to the original budget, under which the schools were operating in September 1979, he said, they spent only $900,000 less than anticipated on administration and $7 million less on classroom operations.

"My conclusions are substantiated by this report," Barry said. "The reductions came right out of school operations last year and they're doing it even more this year. They're hurting people over there." Overall, in the past 15 months, the school system has laid off about 900 employes, most of them teachers.

Parents' groups and members of the City Council have criticized Barry for what they said was his undercutting of the school system, but Barry has argued that it would be irresponsible to give more money to a school system that has not supplied accurate data to support its funding requests.

James R. Boyle, the schools' chief finance officer, said yesterday that Barry's comments on the auditor's report were "not true. I'm satisfied with the report and I reconfirm it." He said that "if the mayor has a problem, it's with Arthur Andersen, not with us."