Federal authorities are investigating whether Robert L. Green, former president of the University of the District of Columbia, improperly took a $1,900 wide-screen television and a $1,300 stereo set that belonged to the university when he resigned from his post in August 1985, according to sources.

The items, purchased with city government or university funds, were determined to be missing during an inventory of the university president's house and were later found to be in Green's possession, the sources said. It is unclear who has possession of the items now.

John F. Mercer, an attorney for Green, said last night, "Bob Green hasn't taken anything. It's ridiculous to say that Green took anything. He is not a thief. We've gone over every transaction that he made at the university and, based on that, we say he has not taken anything."

Mercer said there may have been what he called an exchange of items between the university and Green after Green left, but Mercer said that would have been part of the usual settling of affairs when a university president resigns. "I guess he returned some things and the university had some things," Mercer said.

Green, 54, who lives in Cleveland, could not be reached for comment. He resigned under pressure as UDC president at the end of a three-month controversy over his handling of university funds.

Edward G. Holland, who was an acting associate vice president under Green, said yesterday that Green and his wife Lettie took the television and stereo with them in November 1985 and that "we were under the impression that it was their property." Holland, who has been detailed to the UDC office of continuing education as a program development officer, said he went through the president's house with Lettie Green, the UDC internal auditor and other university staff members to identify property owned by the university before the Greens left.

Sources said that Lettie Green had identified the television and stereo as the family's property.

Also, sources said that FBI agents seized the property this year.

According to sources, the television was a 42-inch wide-screen Mitsubishi; the stereo set, which came with a tape deck, was a Sansui. Holland said the stereo set was initially bought with university funds, but he declined to comment further.

Other sources said that the stereo and television sets were bought with funds from the mayor's office and that it appears that the money came from the mayor's controversial ceremonial fund. The transaction was handled by Robert Robinson, at the time an aide to Barry who controlled access to the ceremonial fund. A federal grand jury is investigating a number of expenditures from the fund. Robinson has declined to comment on his handling of it.

Sources said that shortly after Robert Green was appointed president in 1983, he asked for the television and stereo equipment, saying he planned to hold faculty and student functions at the president's residence, which is owned by UDC.

The mayor's office provided the funds for the equipment -- along with computer terminals and several staff members -- in an effort to show support for Green, who had been persuaded by Barry to take over the post several months earlier than Green had planned, according to sources.

"It was a legitimate transaction, and nobody thought any more about it," according to one source.

According to sources, Green asked the mayor's office to help provide computer equipment for the president's office because it would have taken months to get it through UDC procurement policies.

The mayor's office spent a total of $126,000 in helping set up Green as UDC's new president, sources said. The funds were repaid during that school year in three payments by a UDC budget official.

The money was used in part to pay salaries for Dwight S. Cropp and three other staff members. Cropp, who at the time served as both an assistant to Green and as secretary of the District under Barry, has appeared before the grand jury at least three times to discuss Green's activities as UDC president and the ceremonial fund. Green, Holland and a number of other District and UDC officials also have testified.

The FBI and the U.S. attorney's office have been investigating Green's activities since August 1985, according to a letter from U.S. Attorney Joseph E. diGenova to university officials. Mercer described Green as an accomplished public servant who "would never take anything that didn't belong to him."

Sources said that it appears that prosecutors are satisfied that there would be no impropriety in the use of the funds from the mayor's office to pay for a stereo and television.

Questions first surfaced about Green's use of university funds in June 1985, when The Washington Post reported that Green had spent $83,200 for parties and receptions and traveled extensively at the university's expense, including trips to weddings and funerals.

Concern among UDC officials over Green's expenditures increased with reports of purchases of new furnishings for the president's residence and consulting contracts for several of Green's former colleagues at Michigan State University, including Cassandra A. Simmons, a former student of Green's.

D.C. Auditor Otis E. Troupe challenged the expenditure of thousands of dollars of UDC funds for consultants, travel and flowers and concluded that Green had misspent at least $13,000 from the so-called representation fund, which is used to pay the president's expenses while on official business. Also, Troupe was critical of how Green spent $11,974 of the $30,000 that was set aside for his transition from Michigan State to UDC.