The state of Virginia has agreed to investigate the death of Donald Ferguson, a 28-year-old Gum Springs man who was arrested and jailed in Fairfax County and died shortly after at a state hospital, three county Republican leaders who requested announced yesterday.

"Our basic concern is that the people of Gum Springs and of Fairfax County -- and more, Mr. Ferguson's family -- get the facts," said Republican John F. Herrity, chairman of the Fairfax board of supervisors.

Herrity said the probe will be handled by two state agencies under the cabinet-level secretaries of public safety and human resources.

Herrity was joined by fellow Republican delegates Warren E. Barry, whose southern Fairfax district includes Gum Springs, and Vincent F. Callahan Jr., who represents northern Fairfax.

The Ferguson case has become a cause celebre in Fairfax. Republicans and Democrats have accused each other of exploiting the case for political advantage in an election year.

Ferguson died Dec. 8, 1978, of kidney failure at Western State Hospital in Staunton, Va., 110 miles southwest of Fairfax, where he was taken two days after he developed delirium tremens (alcohol withdrawal) at the Fairfax jail. He had been arrested six days earlier by Fairfax police and charged with tampering with an auto.

On Aug. 9, an unofficial citizens group led by three prominent Northern Virginia Democrats called for the immediate resignation of Republican Sheriff James D. Swinson, who runs the jail.

Swinson, who decided earlier this year not to seek a fifth term, rejected the panel's recommendation as "political bunk."

There was some confusion yesterday as to who would be conducting the investigation, and whether it would actually be an "investigation" or "inquiry."

Herrity, Barry and Callahan said a "broad-based investigation" would be conducted under the auspices of two of Gov. John Dalton's cabinet secretaries -- Selwyn Smith of public safety and Jean Harris of human resources.

But Harris said in a telephone interview: "At this point, I have no role. You're giving me the first information I've had on this incident . . . I'll have to check with Secretary Smith to see what's going on."

Western State Hospital is under the Department of Mental Health and Retardation, over which Harris has authority.

Callahan said that he and Barry had met on Monday with Dalton to request the state probe on Monday, and "what we're doing has his approval."

But the governor's press spokesman, Paul G. Edwards, in a telephone interview referred several times to an "inquiry." "'Investigation,'" he said, "is a loaded word.It has legal implications."

Herrity repeatedly referred to an "investigation" by professional staff "with subpoena powers . . . Once the facts are found out, we've got to let the chips fall where they may."

Barry said the director of the Department of Corrections, Terrell Don Hutto, told him "we've had many [correctional] institutions in Virginia where there have been problems with the transportation of prisoners to hospitals.

Barry said the investigation would look into not only the circumstances surrounding the arrest, jailing and death of Ferguson, but into procedures at the state's correctional institutions and hospitals.

An investigation of the Ferguson case earlier this year by Fairfax Commonwealth's Attorney Robert F. Horan Jr. cleared Swinson and his staff of criminal wrongdoing, but said that Ferguson wasn't given medicine led in food droppings and his own vomit.

Harris said both she and Smith "are invesitgating -- 'looking at' is a better way of putting it -- the need for additional local resources" when prisoners have to be hospitalized.

Fairfax has no public detoxification facility. Fairfax Hospital has an 11-bed unit that, according to a spokesman, is "100 per cent filed up most of the time."

Swinson said the jail had sought to have Ferguson admitted, but was told by the hospital that there was no room in the detoxification unit.

A hospital spokesman said, however, there was no record of such a call, and that even if the detoxification unit was filled, an inmate suffering delirium tremens could be treated in another unit if his admission was authorized by a physician.