Harvard University recently agreed to repay the federal government $4.6 million after a dispute over who should pay the salaries and overhead expenses of professors working on government contracts.

Four campuses of the University of California are battling the Health and Human Services Department over $1.8 million that federal auditors contend was improperly charged to government contracts.

Across the academic landscape, universities are experiencing more government monitoring of their federal research grants and contracts. They are finding that expenses that they once routinely billed to the government are being "disallowed" by auditors, forcing the universities to refund millions of dollars.

The conflict reflects three different priorities: a government facing tight budget pressures, university administrators who want to recoup a fair share of the costs of research, and academics concerned with maintaining freedom unfettered by bureaucracy.

"They are more strict, and tougher," said James Lesch, director of Michigan's division for research and development administration.

"What's happened in my view," said Lesch, "is that the administration has declared that overhead is taking a larger and larger share of total research dollars. And Congress is obviously looking at how we're acting as stewards of that money. So they have been clamping down on the auditors, saying you've got to audit more often, and you've got to be more strict."

But Henry G. Kirschenmann Jr., deputy assistant secretary of HHS for procurement assistance and logistics, replied, "We've got to be sure as civil servants that taxpayers are not being overcharged.There's paper work involved, but . . . we're funding something in excess of $3 billion a year in research and we have a responsibility to account for that money."

The principal difference between the two sides centers on overhead, the "indirect costs" associated with a federal grant or contract.

For example, a professor who receives a $1 million research grant may incur more expenses than that. He uses space on university property, with related utility costs, for which the government is billed. He may have to buy special equipment, which also would be charged to the government. And to complicate the matter still further, the professor may be receiving money from several other sources for the same project and may be conducting unrelated projects in the same space with the same equipment.

The "indirect" or overhead costs that were charged to the government increased from about 15 percent of each grant in 1966 to almost 30 percent in 1981.

One way the government has tried to control the escalation in overhead costs has been to require "effort reporting." It requires researchers to account for all of their time on campus and to specify whether it was spent on teaching, research, administration or whatever. But professors strongly objected, arguing that they could not divide their time so neatly. Yale University mathematician Serge Lang, for instance, made headlines in 1982 when he refused to sign an "effort" form and Yale turned down a $30,000 grant rather than force him to do so.

Lang has become something of a crusader against federal officials and their "effort reporting" requirements, which are enshrined in Office of Management and Budget Circular A-21. But on this issue, the faculty members part ways with the university administrators, who are more worried about new efforts to enforce cost-sharing rules and new auditing procedures.

Harvard, for example, traditionally has paid the entire salaries of its tenured professors, not allowing them to take part of their salaries out of grants. But HHS auditors, reviewing all federal research money to Harvard between 1974 and 1981, told the school that if it wanted to pay professors' salaries it also had to pay part of the overhead costs for their federal research.

Said Thomas O'Brien, Harvard's financial vice president: "We object to that as bad public policy. We just think that's counter to congressional intent and a strictly narrow interpretation of the rules."

Stephen Selby, director of the financial analysis division of the University of California system, is more worried about a new requirement under which universities must pay for a private audit every two years, allowing federal auditors to selectively "parachute" in when they spot a potential problem.