Enrollment in the District's public schools cannot be verified for the last five years because computer tapes with those statistics have been erased and backup paper files are in disarray, an audit commissioned by D.C. school officials concludes.

In the records that were available for study, the auditors said they discovered "ghost" classes apparently had been created at four schools, inflating the enrollment figures that help determine how much money a school gets.

School board members, who paid an accounting firm $100,000 to try to unravel months of controversy about the accuracy of the school system's enrollment figures, have reacted to the audit with outrage. In a tense session with Superintendent Andrew E. Jenkins late Tuesday, when a draft of the audit was presented, several board members asked repeatedly whether a coverup had taken place.

"When records are missing, it can lead you to believe that someone was trying to hide something," said board member R. David Hall (Ward 2). "We don't know yet. Once again, it could just be extremely poor management."

Meanwhile, board member R. Calvin Lockridge (Ward 8) said that the board had been assured in May, when the school system conducted its own enrollment audit, that the computer tapes were in order. "Now we're told that things disappeared," Lockridge said. "Something's going on."

Last night, after they left a meeting of the school system's top officials, board president Nate Bush (Ward 7) and Jenkins disputed some of the audit's findings.

They said only some of the system's computer tapes had been erased, that it occurred accidentally, and that there are other computer records that can be used to help verify school enrollment since 1985.

The size of the school population -- now listed at 81,300 students -- has provoked intensive debate since Feburary, when it was revealed that school officials had asked the city government for a budget based in part on an overcount of 6,500 students.

The disclosure prompted D.C. Council members to ask whether the school system's half-billion-dollar budget, and its teaching force, should be reduced. The new audit, which the school system hired the accounting firm of Deloitte & Touche to conduct, was intended to help clear up confusion about when enrollment dropped, and how it apparently went unnoticed.

Jenkins declined to address the audit's findings last night, but said, "certainly I want people to rest assured that no one here has covered up anything." He also said he was confident that no one had deliberately padded enrollment figures in the four schools cited in the audit.

"We have clear differences with the audit as to what happened," Jenkins said. "I think people are moving too fast to make certain assumptions."

Officials at Deloitte & Touche would not comment yesterday on the audit, which began two months ago. In their report, auditors say they were unable to use computer records the system compiles each October when its formal student head count is taken.

That count begins in every city classroom. Teachers are asked to hand their rosters to a school clerk, who then types the names and class tallies into a computer connected to the school system's headquarters. There, officials are supposed to collect and organize the city's enrollment -- which has a large role in determining how much money schools receive.

Yet in the report, auditors said they saw scant evidence of organization. The computer disks that contain the vital October numbers from fall 1985 to fall 1988, they said, no longer exist because someone apparently typed other data over the enrollment numbers -- thus erasing them.

But the audit also offers broader indictments of school system management, concluding that no official seemed to have authority over the enrollment count and that there are few controls designed to double-check student tallies.

"The report shows that no one has been in charge," board member Hall said. "It clearly shows that even the most elementary management decisions are not being made."

The report recommends that the system count students manually this fall, revamp its computer system, establish more ways to catch errors, and increase training for all of its data entry clerks.

Hall and several other board members said they feared that the audit would further erode the system's credibility, but Bush suggested it will improve the system's image because officials are "making full disclosure" of past errors.

The latest error, the report said, was the system's current enrollment count of 81,301 students. Auditors said they found 80,382 students. They attributed the discrepancy to instances at four schools where it appeared that enrollment had been inflated. The four schools are Anacostia, Coolidge and Spingarn high schools and Hine Junior High School.

At Coolidge, a graduating class was carried on the rolls for two years; at Hine, several classes of students were listed that did not exist. What occurred at the two others was not made clear. The auditors made no attempt to determine whether those overcounts were deliberate, but Bush said last night he will investigate.

"No one knows what happened, and it's frustrating as hell," said board member Wilma R. Harvey (Ward 1). "This puts our credibility in serious danger."

The audit marks the second time this year that D.C. enrollment data have been investigated. The first assessment, completed by an internal team that Jenkins appointed last spring, concluded that top school officials had deliberately withheld statistics from the D.C. Council that showed a steep enrollment drop.

Until then, school officials insisted that their failure to disclose the accurate numbers had been inadvertent.

The first review of enrollment data also painted a portrait of widespread school system incompetence. It said that one of the school system's three deputy superintendents, Arthur G. Hawkins, told a budget director to "pull out" the lower enrollment figure from documents the council had requested.

Bush said last night he hopes to resolve the points of contention the system has with the Deloitte and Touche audit in the next few days.