Reporters began pestering Charles L. Dempsey in February, shortly after the White House asked him to be part of the team to help clean up the Environmental Protection Agency.

The reporters wanted to know if Dempsey had uncovered any wrongdoing in the office of the EPA's inspector general. "Yes," he replied--and they could read about it in his semiannual report to Congress in May.

Those who know Dempsey say the episode tells much about the veteran federal watchdog, who has been sniffing out fraud, waste and abuse--primarily in the government's housing programs--for 26 years.

Dempsey, who left the EPA last month to return to his job as inspector general at the Department of Housing and Urban Development, seems to have become the Reagan administration's favorite detective when it finds itself in a jam.

When the Agriculture Department's inspector general was accused of misconduct last year, the White House sent Dempsey to investigate.

A spokesman for the Office of Management and Budget said the White House has turned to Dempsey on politically sensitive probes because of his experience and reputation for nonpartisan investigations.

Like the straight-faced Sgt. Joe Friday in the old Dragnet television series, Dempsey has a simple philosophy: "Our job is to collect and present the facts. It's that simple."

Dempsey's probes of top officials at HUD have been tough. He accused Donald I. Hovde, then the department's undersecretary, of improperly using a government car. He also asked the Justice Department to prosecute E.S. Savas, a HUD assistant secretary who Dempsey claims used federal employes to proofread and partially type a personal manuscript. Savas has been placed on leave while that investigation is conducted.

The government has experienced a number of housing scandals over the years and Dempsey has investigated most of them since he joined the government in 1957 as a deputy investigator at HUD's predecessor, the Housing and Home Finance Agency. Before that, he worked full time in the agency's mail room for three years while attending night school at Georgetown University.

"I've seen the IGs go from being the illegitimate kid at the family picnic to having management say, 'Hey, we need you,' and that's nice to see," said Dempsey, who now oversees a budget of $22 million and a staff of 513, including 335 auditors and 115 criminal investigators.

Despite such progress, the government's watchdogs still walk a precarious line.

When President Reagan took office, he fired all 16 inspectors general--including Dempsey. The president later rehired Dempsey and five others, but the message was clear: IGs might not consider themselves political appointees, but they served at the pleasure of the White House.

Dempsey didn't like it when he was fired. "I'm not a political appointee," he insisted. "I am a career investigator."

But he has justified the firing in his own mind, he said, by deciding that it was the only way for Reagan to "make sure he had the kind of people in office that he wanted."

Dempsey said he never has had a political problem at HUD, even though he has worked for seven secretaries who "had very different personalities and styles."

"I've been lucky," he said. Some in HUD, however, say Dempsey's low-key style and tough reputation have been the key to keeping politics out of HUD investigations.

"One of the first things that you have to do is read them HUD secretaries the law," Dempsey said, thumbing through a tattered copy of the Inspector General's Act of 1978 that he frequently carries with him.

"Neither the head of the establishment nor the officer next in rank shall prevent or prohibit the IG from initiating, carrying out or completing any audit or from issuing any subpoena," he read from the law.

"Now, that's the law, and you say to them, in a polite way, of course, 'If I am asked by anybody to stop an audit, stop an investigation or stop a subpoena, I'm going to turn it over to the attorney general and the Congress, and you might as well know it.'

"The really smart ones quickly understand that an IG can help them by keeping them clean and they cooperate," Dempsey said.

And if they don't?

Then, the IG continues to go about his job quietly and reports his problems in his semiannual report to Congress, Dempsey said--"just like the IG act provides."

Not everyone has as much faith in the system as Dempsey does.

"I think Charles Dempsey is doing a pretty damn good job," said Al Louis Ripskis, a HUD employe and gadfly who publishes an investigative newsletter that often is critical of his agency. "But he can give the secretary a report an inch thick and if the secretary doesn't do anything, that's the end of it."

For instance, Ripskis said, HUD Secretary Samuel R. Pierce Jr. let Hovde refund $3,149 to the government and took no disciplinary action against him even though Dempsey originally reported that Hovde had misused at least $6,845 in taxpayers' money.

Dempsey insisted, however, that the IGs have "just the right amount" of power to do their jobs. An IG, he explained, is like an ombudsman at a newspaper. "It's his job to investigate readers' complaints and make the editor aware of the problems," Dempsey said. If nothing is done about those problems, it's not the ombudsman's fault--it's the editor's, he said.

"You set your standards high, you bring in the best people, you make sure that they aren't political, and then you do your job," Dempsey explained. In most cases, he said, "the system works."