D.C. Fire Chief Theodore R. Coleman agreed under pressure yesterday to give a House subcommittee a copy of a $24,000 management report on his department, which his office earlier had said did not exist.

Some of those interviewed as part of the management study, conducted by an outside consultant, said they were critical of Coleman's leadership. Coleman told a reporter in late March that he had "destroyed portions" of the consultant's report because "they were no good to me."

But in response last month to a Freedom of Information Act request by The Washington Post, the department said "no written documents of the management study were submitted" by the consultant.

Rep. Julian C. Dixon (D-Calif.), chairman of the House Appropriations subcommittee on the District, asked Coleman three times whether there was a written study document before the chief stated, "there was a report."

Reached at his home last night, Coleman said that the report he referred to in his testimony consists of notes taken by himself during a series of meetings with the consultant, "and maybe some pages the consultant had written some things on." He said that what he destroyed were notes "that I had written myself . . . that I no longer needed."

Dixon noted that Rep. Stan Parris (R-Va.), who has a number of city firefighters living in his district, had asked that the management study be submitted for the record, but Dixon said he would not request that.

Later, however, Rep. Lawrence Coughlin (R-Pa.), ranking minority member, asked Coleman to submit it for review by the panel on a confidential basis, and the chief agreed.

He said he had asked for the study to "get a feel for how to create more cohesiveness" in his department.

Subcommittee members also pressed Coleman on why his department has failed to buy new face masks for firefighters when Congress has provided $372,000 since 1982 for the purchase.

Officials of the firefighters union said that the old breathing apparatus is effective for a maximum of 30 minutes and that new masks would allow them to work for an hour without fear of smoke inhalation.

Coleman said the department should get some new masks next month and that there had been some problems getting the bids out.

The fire department's fiscal 1986 budget calls for only $522,000 in overtime for the 1986 fiscal year when in the first three months of 1985 alone overtime costs were $1.2 million, Dixon pointed out.

"That doesn't make any sense," the chairman said, adding that the fire department has underbudgeted overtime every year since 1980.

Coleman said it would be different in the next fiscal year, however, because the department hopes to resolve litigation over its hiring plan, which has been challenged in court as giving blacks unfair advantage over whites. This would enable the department to fill a number of vacancies and reduce overtime, he said.

Union officials, however, said the department had used this reasoning for the last five years. In the meantime, firefighters have had their vacations canceled with as little as a day's notice because of the unfilled jobs, they said. The union officials said there are more than 120 unfilled firefighting spots, or about 10 percent of the authorized level, and 72 vacancies in the ambulance service.