(CNN) -- Who killed and decapitated an 88-year-old Georgia man, and where is his 87-year-old wife?
Russell Dermond's death and Shirley Dermond's disappearance are mysteries detectives are trying to unravel -- and fast.
"We need to assume, or at least pray, that Mrs. Dermond is still alive, and we desperately need to know her whereabouts," Putnam County Sheriff Howard Sills said Thursday.
Investigators are treating her disappearance as an abduction, he said. There is no indication she's a suspect, and there's "plenty" to indicate she was taken, he said. Her pocketbook, cell phone and vehicle were all at the million-dollar waterfront home where her husband's headless body was found.
Investigators believe Russell Dermond was killed between last Friday and Sunday, and they're still searching for his severed head, Sills told reporters, describing the case as "very unusual" and the most frustrating homicide of his career.
"I don't think it's a random incident. I think for whatever reason these people were singled out for this," Sills said. "They live in the most exclusive neighborhood, or one of the most exclusive neighborhoods, in this county. ... They're on a cul-de-sac in a gated, multimillion dollar resort community that we have no crime in."
Sills said he can't recall a burglary in the neighborhood in his 18 years as sheriff.
The Dermonds' friends hadn't heard from them in days and went to their home in the upscale, gated, lakeside Great Waters community, where they found Russell Dermond in the garage.
"I don't know that that's the murder scene, but there's obviously blood," Sills said.
Authorities have searched Lake Oconee in the vicinity of the Dermonds' home -- turning up only a lawn chair and a Christmas tree -- and sent cadaver dogs into the nearby woods, to no avail, Sills said. Police have also spoken to neighbors, family and friends.
So far, the investigation has turned up little to shed light on the crimes. Investigators aren't aware of any enemies the couple had made, or any reason someone would target them, he said.
"If I had a good, solid lead, guess what? I wouldn't be standing here talking to you," the sheriff told reporters. "The only person who's not a suspect is Sheriff Sills, because I know where I was."
'This has been a shock'
Residents described Reynolds Plantation -- a tony resort community about 75 miles east of Atlanta, which also boasts a Jack Nicklaus signature golf course and a Ritz-Carlton Lodge -- as a safe enclave where people were comfortable leaving their doors unlocked.
"There is no crime in this area, no crime whatsoever," Lillian Butterworth told CNN. "Nothing has ever happened here before, so this has been a shock to us."
Added resident Johnny Wagoner, "It's just a total sense of sadness and confusion on how this could happen here -- and obviously a great deal of concern for Shirley and our prayers and hopes that she will be found."
The 3,300-square-foot home where the Dermonds have lived since 1994 is valued at more than $1 million and sits on Lake Oconee, in the bucolic Great Waters neighborhood of Reynolds Plantation.
Off a moderately trafficked rural road, a divided, two-lane road lined with trees and a white fence winds through large, green expanses of tall grass, past a guard house into the neighborhood.
At this point, investigators don't know whether the suspect or suspects approached the home by land or via the lake. Sills said it isn't uncommon to see fishermen casting lures in the middle of the night.
Without any clear leads as to Shirley Dermond's whereabouts, he said, investigators are now asking the public for help.
Shirley Dermond is 5-foot-2 and weighs 148 pounds. She has gray hair and blue eyes. And she is believed to be in danger, Sills told local media. Anyone with more information should call the Putnam County Sheriff's Office at 706-485-8557.
Details of the case have baffled investigators.
"You've got such unusual circumstances here," Sills said. "If it's an abduction, you would expect some sort of extortion demand. If it was an assassination, you'd think both bodies would be there. And then you have, totally, nothing in their background that indicates anything like this, and then the area where it happened is not indicative of any type of homicide."
Couple was 'sweet as can be'
A Georgia Bureau of Investigation source confirmed the bureau was conducting Russell Dermond's autopsy but wouldn't comment further.
The FBI also is assisting and, likewise, reticent, saying only that it "is providing limited support based on the needs and requests from Putnam County authorities," according to Stephen Emmett, spokesman for the FBI's Atlanta office.
Meanwhile, the sheriff said, rumors have been flying in the small community.
He told CNN earlier Thursday that information suggesting authorities had found parts of Shirley Dermond's body were "totally false" and asked CNN to "help stop the false reports, as they are interfering with our investigation."
Little else is known about the couple, both of whom were born in New Jersey. Police and friends are at a loss for why they would be the targets of such violence.
Compounding the mystery is that the home was pristine. There is no sign of a break-in, a scuffle or anything missing. Their vehicles were at the home, police said.
Russell Dermond has paid taxes on a 23-foot boat, which Sills said the couple recently sold, and Dermond reportedly owned fast-food restaurants. Tax records connect him to a Wendy's and a Chick-fil-A.
The Rev. David Key of Lake Oconee Community Church said he has known the couple for about eight years and counts them among his church's 350 attendees. He's "baffled" as to why anyone would commit such crimes against them, he said, as they were grounded, "beloved in the community" and "sweet as can be."
They were active in the church and family-oriented, he said. The Dermonds, who have been married 68 years, had three adult children, he said, as well as grandchildren, though he wasn't certain how many.
"Number one, we are devastated by Russell having died and the violence around that," Key said. "And not knowing what happened to (Shirley). ... It is dealing with the tragedy of what we do know and the uncertainty of what lies ahead."
CNN's AnneClaire Stapleton and John Murgatroyd contributed to this report.