Last June, Dr. Thomas M. Dent III, a Washington physician, pleaded guilty to mail fraud and to filing false medical claims for treating a government worker who actually was in jail at the time.

Under District law, a physician can be barred from practicing medicine here if he is found to have submitted false bills or been convicted of a crime related to his practice. But Dent is still practicing here and still submitting bills to the federal workers' compensation program.

The District agency charged with regulating the city's 9,000 physicians has yet to review his case.

Dent's situation is far from unusual. Officials at the D.C. Commission on Healing Arts Practice, whose responsibility is to weed out corrupt or incompetent doctors, acknowledge that they rarely take action against physicians, even those convicted of criminal fraud. They say they have not acted because they have had no staff to conduct any investigations.

"These cases have been lost between the floorboards," said Dr. Pearl Watson, a private physician who serves as chairman of the Healing Arts Commission. "There are lots of cases like Dent's , but we can't do anything without a staff. Some of these cases are outright criminal."

The commission was given expanded powers in 1977 because of complaints that it was doing little to police the medical profession. This criticism came to a head when the panel appeared slow to act against Dr. Robert J. Sherman, who was charged with performing an incomplete abortion that led to the death of a 16-year-old patient. After a mistrial, Sherman pleaded guilty to perjury in exchange for having a second-degree murder charge dropped.

The commission was made a semi-autonomous agency after it revoked Sherman's license. Since then, however, it has had just one professional staff member and has been operating out of three bare rooms in a basement office on G Street NW. It has revoked only two doctors' licenses, one of which has since been restored, and has failed to act on a backlog of about 20 cases involving either convictions of doctors or public complaints about physicians.

In 1980, after commission officials insisted that their $200,000 budget be increased so they could hire an investigative staff, Mayor Marion Barry's office agreed to more than double the medical licensing fees the panel collects. But although these fees now bring in about $700,000 a year, the city has placed all the extra revenue in its general treasury.

City budget director Gladys Mack said she was "not aware of any difficulty" at the commission and was not convinced the panel had a pressing need for more staff. She said some technical problems had delayed the hiring of two investigators until January, but added: "Some of the reason they didn't have any staff was due to their own lack of urgency."

Mack said the city's licensing fees are designed to cover operating costs and to provide revenue to the city, not to boost the budgets of the agencies that collect them. "The money isn't managed that way," she said.

The case involving Dent, one of at least seven D.C. doctors who in the last four years have been convicted or pled guilty to criminal charges, is hardly an obscure one that somehow escaped the panel's notice. Dent received widespread publicity last summer when the Senate Permanent Investigations subcommittee used his case at a hearing to demonstrate how the federal workers' compensation program was vulnerable to fraudulent claims.

A federal grand jury indicted Dent on 15 counts of mail fraud in connection with a scheme in which he allegedly sold at least $10,000 in inflated medical bills to lawyers, who in turn submitted them to private insurance companies for payment. The indictment charged that Dent exaggerated several patients' injuries and prepared false bills for X-rays and other treatments he never performed.

Ten months ago, Dent pleaded guilty to one count of mail fraud and one count of submitting false bills for the Labor Department's workers' compensation program, which makes payments to injured workers. In that instance, the indictment charged that Dent submitted 21 bills for providing muscle relaxants and ultrasonic treatments to a Government Printing Office employe, who was later found to have been in a Virginia jail during part of the time he was allegedly under treatment.

When Dent was sentenced, the Healing Arts Commission had the legal authority to "These cases have been lost between the floorboards. There are lots of cases like Dent's , but we can't do anything without a staff." ask the judge to revoke his medical license. But P. Joseph Sarnella, the commission's full-time director, said the U.S. attorney's office did not notify him in time to make such a recommendation.

U.S. District Judge John Garrett Penn gave Dent a suspended sentence of 16 to 48 months in prison. He also fined Dent $9,000, placed him on three years' probation and ordered him to provide 250 hours of community service.

The Healing Arts Commission still could have conducted its own investigation of Dent, taken testimony at a formal public hearing and decided whether to fine him or bar him from practicing medicine. It also could have used the court record as evidence against him.

Sarnella said he has been too busy with the panel's ongoing business of licensing doctors to examine Dent's conviction.

Three months ago, he said, city officials finally allowed him to hire two staff investigators and two clerical workers. He said he recently asked the investigators to look at the 20-case backlog that has languished over the last two years.

Dent's case "didn't just slip through the cracks," Sarnella said. "I just didn't have any staff to do anything with it."

Since the Healing Arts Commission, whose 11 members are appointed by the mayor, was made independent from the city's licensing agency, it has successfully urged judges to take away the licenses of two doctors convicted of illegally dispensing narcotics. But in two other cases, when judges declined to revoke the licenses of doctors convicted of mail fraud, the panel took no further action.

The commission has held just two public hearings in the last four years. In 1979, it revoked the license of Dr. H. Barry Jacobs, who was convicted for signing a blank prescription form that was used to dispense drugs. And in 1980, it revoked the license of Dr. John B. Fegan, who pleaded guilty to two counts of illegally distributing Dexedrine and other drugs. The panel restored Fegan's license last month.

Meanwhile, the Senate subcommittee, chaired by Sen. William Roth (R-Del.), is demanding to know why the workers' compensation program has continued to pay Dent and other doctors who have been convicted of fraud. The subcommittee found, for example, that the program paid Dent last fall for at least six bills covering heat treatments for an Internal Revenue Service employe who switched to Dent from another doctor. Dent said this week he would have no comment on the matter.

Ralph W. Hartman, who runs the program for the Labor Department, also declined to comment.