The price tag for defending University of the District of Columbia President Robert L. Green against claims that he has misspent university funds is mounting, with the university paying a $15,000 tab for the first of two audits by an outside accounting firm as well as $190-per-hour fees for a special attorney hired by university trustees.

Several board members have expressed concern about the costs associated with the Green controversy, which are expected to double when a second independent audit by the accounting firm is completed later this month.

In a closed-door, two-hour meeting in executive session last Wednesday, the trustees debated the merit of using outside accountants and lawyers to respond to news reports and assertions by D.C. Auditor Otis H. Troupe that Green has misspent thousands of dollars of UDC funds on travel, consulting and personal items.

The board of trustees is currently paying $190 an hour for work by special counsel Vincent H. Cohen, a prominent Washington lawyer, and about $140 an hour to Cohen's assistant for legal work connected with the Green case, according to several trustees who asked not to be named.

Coopers & Lybrand, a national accounting firm, has charged the university $15,000 for its audit of the president's representation fund, an annual discretionary account Green can use to cover expenses connected with his official duties, several trustees said after the meeting. The firm concluded last month that Green had misspent $2,330 of university funds, which since have been repaid.

Based on the firm's report, an executive committee of the board on July 31 voted 3 to 2, with one abstention, to issue a statement in support of Green.

With the audit of the representation fund completed, Coopers & Lybrand is now reviewing the university's postsecondary education account, an $800,000 fund that trustees said will be much more costly to audit because of its complexity and size.

Troupe also began auditing the postsecondary account a few days ago. Until last week university officials had refused to turn over its records to him.

In the executive session Wednesday, board members agreed to continue with Coopers & Lybrand despite the mounting costs and a feeling among some trustees that the accounting firm's conclusions about the representation fund were not significantly different from Troupe's, several trustees said.

Coopers & Lybrand currently holds a $440,000 contract with the District government to perform its annual independent audit of city finances.

The firm was retained by the UDC board after special counsel Cohen wrote a letter three weeks ago on behalf of the trustees to D.C. City Council Chairman David A. Clarke accusing Troupe of leaking information from his draft audit to the press.

Troupe has declined to comment on all aspects of audits in progress.

In addition to legal fees related to the Troupe audits, Cohen is being paid by the board to defend Green and the university against freedom of information suits brought by The Washington Post and The Washington Times, which have sought to obtain records of the representation and postsecondary education funds.

The university also has paid travel costs for three attorneys involved in Green's defense in a sexual harassment suit filed in Minnesota in December. Although university spokesmen have said the lawsuit brought by two women in Minneapolis is a private matter, UDC has paid for attorneys Herbert O. Reid Sr., Thomas Atkins and Ruthie Taylor to fly there to take depositions in the case.

Atkins, a New York attorney and longtime civil rights associate of Green, was retained as Green's personal attorney in the case. Green also hired Atkins as a consultant at UDC to negotiate with the faculty union over a new contract, university officials confirmed.

Reid is special counsel to Mayor Marion Barry and a member of the UDC board. Taylor is the university's general counsel.

Dwight S. Cropp, a university spokesman, said that board Chairman Ronald Brown had authorized Taylor and Reid to make the trip as representatives of the board and the university.

University officials have said that Atkins' trip should not have been paid for by the university and that he will reimburse UDC for $393 in air fare.

In the suit, two women employes of the Minnesota Commission on Human Rights allege that Green harassed them when they were sent by the deputy commissioner to escort Green from his hotel room to a press conference and then to a luncheon where he was to give a speech.

The deputy commissioner, Walter Barwick, was a former student of Green at Michigan State University, where Green was a dean prior to becoming UDC president in September 1983. Barwick invited Green to speak at a Human Rights Day luncheon in Minneapolis, according to sources familiar with the case. Barwick is also named as a defendant in the suit.

Green has vigorously denied the harassment allegations, calling meetings with students, faculty and trustees last spring to assert his innocence.

Sources said last week that both sides are considering an out-of-court settlement.