Twenty-four District of Columbia Interhigh League football coaches and athletic directors have been cited by the school superintendent for misusing thousands of dollars by spending money intended to pay for reconditioning of old high school athletic equipment to buy new gear instead, The Washington Post has learned.

The misuse of money has resulted in a bill for approximately $11,000, for new athletic equipment, that the school system is refusing to pay, according to School Superintendent Vincent E. Reed said yesterday he has informed Mayor Walter E. Washington and the city's legal representatives in the corporation counsel's office that the school system will not pay the money to a New Jersey firm that entered into a deal with coaches to sell them new sporting goods.

The 24 coaches and athletic directors have had letters of reprimand put in their personnel files by Reed.

In question is money allocated for reconditioning of athletic equipment, mostly football helmets, shoulder pads and cleats.

According to Reed, the athletic division of the school system allots about $17,000 annually for reconditioning of equipment, which includes cleaning equipment and making minor repairs to straps and webbing on helmets and pads.

During the 1978-1977 school year, according to officials of the school system's athletic department, only a third of that money, about $6,000, was used to recondition equipment.

The remaining money, about $11,000, was funneled through the reconditioning company that had a contract with the D.C. schools, Olympic Reconditioning Co. Inc. of East Stroudsburg, Pa., to a New Jersey sporting goods firm owned by the brother of the man who represents Olympic in Washington, according to Reed.

Walter Laake, a Langley Park lawyer who represents both Teammate Inc., of Mattawan, N.J., the sporting goods firm that sold the school system the new equipment, and Olympic's agent in Washington, said yesterday he is trying to collect $15,191.02 from the D.C. schools for reconditioning athletic equipment and $3,500 for new equipment, figures differing from Reed's.

Laake also said Reed had underestimated the amount budgeted by the school system for reconditioning equipment. Laake said his client, James Shirgio, who went from high school to high school as the reconditioning company's agent, had a contract with the schools for $25,000 worth of reconditioning old athletic equipment.

The approximately $11,000 paid for new equipment shipped to the D.C. high schools by the New Jersey sporting goods firm, according to several coaches and other sources.

The reconditioning company, Olympic, falsified vouchers and receipts sent to the D.C. school system's budget office, according to superintendent Reed, to coverup the purchase of new equipment.

Both companies deny falisfying and records.

Reed said he met with the president of the reconditioning company last spring after threatening the company with an FBI investigation of its involvement in the scheme if it did not cooperate with the school system's investigators.

". . . After one guy heard the FBI might be involved, he started singing like a bird," said Reed.

"The system had not been shortchanged any money," said Reed. "We haven't paid the balance of the bill and we don't plan to. (Both companies) have threatened us with lawsuits if we don't come up with the money.

"We paid Olympic the amount that we owed them for reconditioning and returned some of the unused (new) equipment to them. Both companies feel we owe them," Reed added. He said the practice in question has been going on for 12 years, involving various firms.

Nik Shirgio, president of Teammate Inc., the New Jersey sporting goods firm, said yesterday that he would not comment on the problems his company is having with the D.C. school system.

Laake, who is trying to collect payment for Teammate's bill for the new equipment, said he and his client met with Reed and other school officials in April to discuss payment for reconditioning and purchasing equipment.

Shirgio said none of the new equipment Teammate delivered to the D.C. schools has been returned and said some of the new equipment shipped to the D.C. school by Teammate was purchased by the schools out of the proper budget for new atheltic equipment. But Laake said the schools are refusing to pay Teammate any of the money it claims it is owed.

Rozelle said yesterday that, when the two players were signed by their present clubs, Jay Moyer, in-house counsel for the NFL, gave copies of the commissioner's written decision to agents for Reese and Crowder. The commissioner recalled that he personally talked to the agents the next day and quoted them as making remarks such as "fine" and adding that their clients "were very happy for the chance to play again."

The commissioner cited the agents as saying they had no complaints and that the players were willing to donate the specified $5,000 to a drug rehabilitation program "subject to our approval."

Rozelle said the arbitration procedure will not prevent Reese and Crowder from continuing to play for their present clubs. He said he interpreted the challenge to his authority as meaning he would not be able to fine, suspend or discipline players for actions off the field "in or out of season," if successful.

When Anthony De Cello, Pittsburgh attorney for Crowder, reported a contract had been signed with the Buccaneers, he quoted the former Penn State player as saying, "I am extremely happy that Tampa Bay gave me a second chance in life. I will not disappoint Tampa Bay, the fans or Commissioner" Rozelle.

According to Laake, his client, James Shirgio, had worked for the Raleigh Equipment and Reconditioning Company of New York City before working for Olympic and had used reconditioning funds to buy some new equipment at that time, at the request of coaches.

Laake said the school system never knew of the plan because Raleigh both reconditions equipment and sells new equipment. But when his client began to represent a firm that only reconditioned equipment, Laake said, problems arose. Laake said coaches asked Shirgio to find a company that would accept money from the reconditioning fund of new equipment. Laake said that Shirgio recommended his brother's firm Teammate, and that Olympic Reconditioning began reimbursing Teammate for the new equipment it shipped to the D.C. schools.

Joe Saliani, controller of Olympic Reconditioning Co., said his company did not do "anything not signed for in writing by coaches and athletic directors.

"We did any and everything they asked for," he said. "We were doing them a favor, helping them to get new stuff. They said they couldn't have got it any other way."

Saliani said there were "no kickbacks" to coaches for using the reconditioning fund to buy new equipment.

All of the nine coaches and athletic directors who were interviewed concerning the matter acknowledged that they have used money allocated for reconditioning to purchase new equipment. The coaches, along with school administrators, said, however, that only one coach used school system money to buy sporting goods for himself.