The D.C. inspector general's office started an investigation yesterday of travel reimbursements by the city government to Cora Wilds, chairman of the District's Boxing and Wrestling Commission, while Mayor Marion Barry's senior aides said privately that Barry should dismiss her and appoint a new chairman.

The Washington Post reported yesterday that Wilds, 42, had charged the city for about $3,000 in travel expenses in 1983 and 1985 at the same time that an international boxing organization had paid the expenses.

In addition, the Post reported that the treasurer of a second organization was "90 percent sure" that his group had paid most of Wilds' expenses to meetings in Bangkok, Aruba and Montreal. The city also had reimbursed Wilds for expenses incurred on those trips, according to city records.

The Post reported that Wilds, after being questioned by the newspaper twice about the expenses, returned $2,745 to the joint International Boxing Federation-United States Boxing Association by overnight air express on Tuesday. Robert W. Lee, president of the organization, said Wilds included a note saying the money was to repay the IBF-USBA for travel reimbursements.

Lucenia Dunn, a spokeswoman for the D.C. Department of Consumer and Regulatory Affairs, confirmed yesterday that Wilds' records from the boxing commission had been provided to Inspector General Vernon S. Gill. Gill declined to comment yesterday.

Sources said that Barry had not decided yesterday whether to ask for Wilds' resignation. Wilds' second three-year term on the commission expired in January, and because she has been serving since then at Barry's pleasure, the mayor could simply name her replacement, the sources said.

According to the sources, several senior Barry aides have said Barry should name a new commission chairman immediately as an indication of his unwillingness to tolerate alleged corruption. Barry appointed Wilds to the commission in 1980.

Barry declined to comment yesterday. Mary Layton, the city's communications director, said Barry "has no statement at this time."

Wilds, who serves on the three-member commission without salary, could not be reached despite several telephone calls to her home, her commission office and her office at the University of the District of Columbia, where she is a political science instructor.

Lee, of the IBF-USBA, and Steve Crosson, treasurer of the World Boxing Council, said their organizations routinely reimburse officials or their organizations for all or part of their travel to group meetings. Wilds was an executive committee member of the IBF-USBA from 1983 to 1985, and she is now a committee chairman of the WBC.

Crosson said Wednesday in a telephone interview from the WBC's meeting in London that he was "90 percent sure" that the group had paid for half of Wilds' air fare and "most if not all" of her hotel charges during her trips to WBC meetings in Bangkok, Montreal and Aruba during the last three years.