The case of a 28-year-old Fairfax County construction worker, who died after a four-day stay in the county jail during which he was severely ill, prompted the County Board of Supervisors yesterday to order a formal investigation of the death.

The death of Donald L. Ferguson also has brought angry protests from the county's largest black community, Gum Springs, where Ferguson grew up and where he was arrested recently for allegedly tampering with an automobile.

The cause of Ferguson's death is still unknown. What is known is that he was arrested on Dec. 2 and kept in the county jail for four days. During that time, according to jail physician Dr. David M. Abbott, Ferguson displayed symptoms that "looked like he needed hospitalization."

On the recommendation of a jail medic, Ferguson was committed on Dec. 6 to Western State Hospital in Staunton, Va., a state mental institution. Shortly after midnight on Dec. 8, Ferguson died at the hospital. At autopsy has so far been unable to determine the cause of death.

Members of the Ferguson's family and other Gum Springs residents, meanwhile, say that cannot understand why a strong young cement worker would end up dead 150 miles away from home. Family members said yesterday that no one attempted to contact them when Ferguson was commit ted to the hospital and that they found out about the death three days after it happened.

"If they could come down here [to Gum Springs] to arrest him," asked Howard Ferguson, Donald Ferguson's brother and a licensed bail bondsman, "why couldn't they come back here to at least tell us what they planned to do with him?"

Fairfax Sheriff James D. Swinson, who runs the jail and who began his own investigation into the death yesterday, said Ferguson was suffering from delirlum tremens, an alcohol withdrawal reaction, when he was brought to the jail.

Swinson said Ferguson hit his head against a glass window in his cell and had to be restrained. The commitment order, signed by jail medic Clarence A. Fry, a county magistrate and a court-appointed lawyer, said Ferguson was "disoriented and not able to care for himself."

Coen C. Plasberg, director of Western State Hospital, said yesterday that Ferguson was admitted and sent to the medical unit because of delirium tremens.

"He had scratches and minor abrasions over his eyes, as well as minor abrasions on his elbows, shoulders and knees," Plasberg said. He said he couldn't determine what caused the injuries.

Plasberg said he thought it unusual that a man suffering from severe delirium tremens would be kept four days in a county jail. "DT's are a medical problem that should be treated in a hospital," Plasberg said.

The cause of Ferguson's death cannot be determined until toxicology tests are conducted in Roanoke, Va., sometime this week, Plasberg added.

In the Gum Springs area, where relations with county police at the nearby Groveton District Station have often been strained, citizens yesterday were alleging that Ferguson was treated callously and that police paid no attention to the feelings of Ferguson's family.

John D. Blunt, a contractor who employed Ferguson and who owns Fairfax Waterproofing Inc., said the police do not respect the feelings of poor blacks in Gum Springs. "If you own a business, like me, they give you some respect, but if you are not somebody you catch hell," Blunt said.

Supervisor Warren I. Cikins (D-Mount Veron), who brought the question of Ferguson's death before the board yesterday, said that police-citizen relations in the area have traditionally been bad.

Police Chief Richard A. King said yesterday that Ferguson, who was held in custody after his arrest for failure to pay a court-imposed $50 fine for battery theft, was in good condition when police turned him over to the county jail. If anything happened to Ferguson, "We [the police] didn't do it," King said.

Members of Ferguson's family and of the his employers said yesterday that Donald (Duck) Ferguson did drink quite often, but that he never went to work drunk. They said alcohol did not interfere with his life.

The young man's family also complained yesterday about the inability to reach Donald Ferguson after his arrest.

Howard Ferguson Sr., his father, said that he went to the county jail on Monday following the Saturday arrest. "I asked for a Donald Ferguson and the woman deputy told me, no, he wasn't there. I couldn't do nothing but stand there in the jail and look foolish," Ferguson said.

Swinson said yesterday he is investigating whether the senior Ferguson was told that his son was not in the jail.