Goaded into action by a legislator-critic, Virginia auditors are investigating a sprawling state agency that spends more than $60 million a year on programs that include finger painting, picture hanging and flower arranging.

The investigation is directed at the Extension Division of Virginia Polytechnic Institute and State University, the bureaucratic home of the county extension agent and the fountainhead of costly government services to farm and home.

The extension agent has been romanticized in America, especially in the South, as the amiable harbinger of scientific agriculture who taught poor farmers, black and white, to coax better yields of corn and cotton from tired land. So thoroughly associated with good deeds is the extension agent that no one was surprised to see one befriend Alex Haley's fathe in the television series Roots II.

But State Del. Frank M. Slayton (D-Halifax) a member of the House Appropriations Committee, has charged that the Virginia extension service has taken a 1966 state law as a mandate for "make work" government. Half of the extension service's work, Slayton charges, now consists of programs outside agricultural assistance and home economics -- the fields for which the service was organized.

Extension service officials dispute Slayton's figures, saying that no more than $3 million to $4 million of their budget is involved in "non-traditional" work.

There is no dispute, however, that the Virginia extension service has become a flourishing bureaucracy. Some items:

Last year, an extension employe was dispatched from Virginia Tech in Blacksburg to Fairfax County to conduct a seminar on how to conduct yard sales.

Another made a two-day trip at state expense from his home base in Blacksburg to Chincoteague on the Eastern Shore to attend a "seafood conference." The conference turned out to be the Seafood Festival, the shore's annual open air celebration of seafood, beer and politics.

In Fairfax, one of the nation's most affluent counties, an extension office force of 33 has as a major part of its mission "helping county residents attain a higher standard of living."

In Fairfax and other subdivided suburbs of Virginia, the Extension Division has nimbly made the transition from dairy farm assistance to "horticultural services." This is lawn and garden advice for homeowners, including free soil testing to determine how much lime should be spread on oak shaded lawns.

Hundreds of extension agents scattered in 112 offices throughout the state serve as members or officers of agribusiness boards such as the Virginia Pork Producers Association and the Virginia Farm Managers and Rural Appraisers Society, private interest groups with a stake in state legislation. Slayton believes this poses a potential conflict for extension employes.

Free services to private businesses included a recent trip by an extension employc to Roanoke to help a bottling company design a wall to ward off flooding from the Roanoke River.

Extension employes regularly serve as "educational advisers" to such business giants as J. C. Penney, Johnson Wax and Rubber Maid. The same agents are free to accept paid consulting jobs with private companies. Extension Division Dean William Van Dresser said the agents do this work "on nights and weekends."

Slayton contends that the Extension Division is a classic example of a self-nourishing bureaucracy that has strayed from its original purpose to sustain its growth.

"I'm concerned that they've got all these little make-work projects that they never intended to do," he said. "Half their programs have nothing to do with agriculture and home economics. They've gone into the core cities and they're teaching everything from finger painting to how to transfer pictures on to T-shirts.

"They're duplicating the work of other agencies and private groups and they're doing a lot of things government has no business doing at all. As expensive as government has gotten, we need to take a hard look at eliminating some of these services."

Van Dresser said in an interview that all of the activities of the Extension Division that have been questioned are "legitimate parts of programs that have been approved by state, federal or local governments.

"The amount of time and effort we spend on agricultural programs has ever increased," he said, "but we have expanded into other areas to meet new needs. All of these things can be legitimized in the context of our goals.

"The emphasis on lawn, garden and park care grew out of the ecological concerns such as those expressed by Lady Bird Johnson" for beautifying urban areas, Van Dresser said.

He defended the corporate advice provided by the service as "an important part of the interaction between consumers and industry."

Slayton's complaints during Appropriations Committee hearings last summer finally resulted in a formal investigation by the Joint Legislative Audit and Review Commission. Its probe is headed by William Landsidle, who directed a recent investigation that found management of the state pension system to be in shambles. The commission's report on the Extension Division is not expected before July.

State Secretary of Education J. Wade Gilley also had convened a task force to study the Extension Division, but suspended its activities after the commission began work. Slayton complained that Gilley's inclusion of Van Dresser and other division officials on the task force amounted to "posting the fox to guard the henhouse."

Gilley said he views the Extension Division as a classic example of a state agency that has been permitted to expand its spending in every two-year budget perios without a rigorous analysis of existing programs. "As with other agencies," he said, "its always been a matter of coming in and persuading a governor that you need a certain amount of growth."

The result, Gilley said, has been per capita expenditures in Virginia that rank at the top in the nation.

He said he believes 30 percent or 40 percent of the $60 million budget goes for programs other than traditional farm and home services.

Slayton said the budget could be cut in half without affecting needed agricultural and home economics programs.

Their estimates represent a range of savings from $18 million to $30 million in state and federal funds.

In addition to the state extension budget, which includes federal funds, cities and counties contribute millions more to the program.

Fairfax, for instance, is spending $289,000 on extension service in the current fiscal year and is proposing and increase to $307,000 next year. Most of the county money goes for all or part of the salaries of 21 of the 33 Fairfax employes.

"We don't have a full-blown review of the extension program going," Fairfax budget official Timothy Brown said. "It's not peanuts, but in a total budget of $377 million, it's not a large enough program to merit a lot of management time for analysis."

"All of our programs have been approved at one level or another of government," Van Dresser said. Fairfax County has never questioned our programs."

"There may be a few areas that we need to review," he added, "but we know we have a story to tell."

In rural counties especially, the extension program has a well-developed constituency to resist budget cuts. A veteran administration official, who asked not to be named, said, "To begin with, there are all those agents working in every county and then there are the 4-H clubs."