For nearly three months, the question of who killed the wife and son of Alex Murdaugh, a prominent lawyer in rural South Carolina, has gripped the state’s Lowcountry region as harrowing details of the crime emerged but the police made no arrests.

On Saturday, the mystery deepened further when Mr. Murdaugh himself was shot in the head while changing a tire on the side of the road, according to his lawyer, Jim Griffin, who said Mr. Murdaugh was conscious and able to speak on the telephone from his hospital bed.

Mr. Murdaugh told one of his brothers from the hospital that he had pulled over to change the tire when someone in a truck drove past him, then drove back around and shot him, Mr. Griffin said.

Tommy Crosby, a spokesman for the South Carolina Law Enforcement Division, the police agency that is investigating the original double killing, confirmed that Mr. Murdaugh had been shot in Hampton County, a rural county that borders Georgia, but said he could provide no more details.

Mr. Murdaugh is a lawyer whose father, grandfather and great-grandfather each served as the top prosecutor for a broad swath of the southern part of the state over more than eight decades, forming a legal dynasty that has made people wonder whether they were targeted.

On June 7, he returned to his family’s home in Islandton, a hamlet of fewer than 100 people, and discovered his wife, Maggie Murdaugh, and his son, Paul Murdaugh, a college student, fatally shot.

Since then, questions have swirled about who the perpetrator could be, and the family has received intense scrutiny, particularly over the fact that Paul Murdaugh was, at the time of his death, awaiting trial on charges of boating under the influence related to a 2019 crash that killed a 19-year-old woman who was a passenger.

Documents and videos released since Paul Murdaugh’s death have raised questions about whether the police were sloppy or gave him favorable treatment, though they have denied that. In one case, a passenger on the boat told a Department of Natural Resources officer that Paul Murdaugh had been driving the boat, but the officer wrote in a report that the passenger had said he was not sure who was driving.

In June, Alex Murdaugh pledged a $100,000 reward for information that led to a conviction against whoever killed his wife and son.

His family has said little about the case, though Mr. Murdaugh’s brothers said in a television interview shortly after the killing that the family was “hurting” and that they worried they had not taken threats against Paul Murdaugh over the boating crash seriously enough.

On Saturday, Mr. Griffin said the shooting of his client had only worsened the family’s suffering.

“It’s shocking and very disturbing, without a question,” Mr. Griffin said. “It makes us all wonder what the hell’s going on.”