Since President Reagan took office, the government's 16 inspectors general have been basking in a flattering public spotlight.

The administration has made the IGs' work a top priority and has credited them with saving a staggering $8 billion within the past 12 months by reducing waste, fraud and abuse in federal programs.

But since their jobs were created in 1978, the IGs have continued to be dogged by a tough question: are they as independent as Congress intended them to be--particularly when it comes to investigating top agency officials?

The law requires IGs to report twice a year to Congress, with agency heads allowed only to comment on the reports.

But it also gave agency heads "general supervisory authority" over the inspectors general and told the IGs to make every effort to work as partners with agency administrators.

"The act was designed to enable the IG to function even without the support of or in opposition to an agency head," explained James R. Naughton, a staff attorney to the House Government Operations Committee, who helped draft the 1978 Inspector General Act. "But the IG obviously can do a better job if he has the support of an agency head."

Yet the tie between IGs and agency heads can create difficult situations, Naughton said, especially when IGs are called in to investigate their "supervisory" officials.

For example, Matthew N. Novick, the IG at the Environmental Protection Agency, has spent a large part of the past 12 months investigating charges of misconduct against Administrator Anne M. Gorsuch and her appointees. But at EPA, the agency's general counsel also is the IG's chief attorney and is intimately involved in most of the investigations. That person is Associate Administrator Robert M. Perry, who also is one of Gorsuch's top aides.

After calling in outside counsel, Novick concluded that charges that Gorsuch had given preferential treatment to a New Mexico refinery were unfounded. Novick found that one aide had violated agency rules and referred the charges to the Justice Department. A second Gorsuch aide investigated by Novick has resigned; Novick has sent his report to Justice. However, members of Congress have been critical of the handling of the case.

In another kind of dilemma, Richard P. Kusserow, who holds that job at the Health and Human Services Department, recently had to turn to Secretary Richard S. Schweiker to keep his office from shutting down because of a budget snafu. Schweiker diverted $2.6 million from another HHS account.

In both cases, Joseph R. Wright Jr., deputy director of the Office of Management and Budget and chairman of the President's Council on Integrity and Efficiency, said the IGs' "personal integrity" has kept their relationship with agency heads at "arm's length."

Wright recalled his own experiences as an acting assistant secretary at the Commerce Department. "There was never any question, as far as I was concerned, that the IG at Commerce was at arm's length from us, but we also knew that he wasn't trying to do a 'gotcha' on us, . . . trying to embarrass the secretary. He was part of the management team, in that, he let us know beforehand when problems came up so that we could correct them. But he always reported it and we knew that he would."

Questions about the IGs' political independence first arose when Reagan took office and fired all of the IGs that Jimmy Carter had appointed. "It is vital that I have the fullest confidence in the ability, integrity and commitment of each appointee," he explained. The House Government Operations Committee, however, called the mass firings "abrupt and disorganized" and said Reagan had violated the "intent" of the 1978 law.

Reagan rehired six of the IGs. Three returned to their former jobs, the other three went to new agencies.

Charges of politicking surfaced again this spring when the General Accounting Office said the IGs had inflated the statistics in their biannual progress reports. The IGs had claimed they had saved $2 billion during the administration's first six months. GAO said the figures were inaccurate, misleading and, in one case, "scratch-paper" estimates.

Wright admits there were problems with some of the statistics, but defends their overall accuracy.

Recently, investigations of Commerce Secretary Malcolm Baldrige and Veterans Administration head Robert P. Nimmo raised new concerns on Capitol Hill.

Baldrige has been investigated twice by Commerce IG Sherman Funk, Nimmo by Frank Sato, the IG at the VA. All three probes found that the Reagan appointees had violated federal regulations and presidential directives. In Nimmo's case, Sato said the administrator had violated a federal law barring the use of government funds to pay for a chauffeur.

But Funk cleared Baldrige of any "serious wrongdoing" and Sato delivered his report directly to Nimmo, so that he could time its release, and to the White House rather than to the Justice Department.

That the IGs could accuse Baldrige and Nimmo of wrongdoing proves the investigators were free from political pressure, said Wright.

"If you ask, 'Does the president have the right to hire and fire IGs?' then the answer is yes, so to some extent, they are political," he said. "But the way they are handled and the way they are managed in the council gives them as much independence as they can possibly use."