Police in central Georgia are baffled by a suspected home invasion that left an elderly man decapitated and his 87-year-old wife missing.

On Tuesday, police were called to a house in Putnam County, Ga., where they found the decapitated body of 88-year-old Russell Dermond. Dermond's 87-year-old wife, Shirley, is missing, and police fear may have been kidnapped or killed.

"I don't think it's a random incident. I think for whatever reason these people were singled out for this," Putnam County Sheriff Howard Sills told reporters Thursday. "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 added that there hasn't been a murder in the area for more than a decade, and it's been at least 18 years since the last home invasion.

Security cameras in the gated community weren't working, though security guards didn't report anything unusual on Friday or Saturday, when police believe the crime took place. Sills said it's possible the culprits accessed the house via nearby Lake Oconee, which spans four counties.

Most, if not all, of the Dermond's valuables—their cars, cell phones, jewelry, and wallets—were left behind.

Authorities have used SONAR to search the lake and sent cadaver dogs into the woods near the Dermond's home, but so far have found no signs of Shirley's body.

"We don't have anything to track her other than the image of her we've given out for the public to see," Sills said."We've put all of our resources into this, we've been assisted by the FBI."

As of Thursday evening, there were no major leads or suspects in the case. "If I had a good, solid lead, guess what? I wouldn't be standing here talking to you," Sills told reporters Thursday. "The only person who's not a suspect is Sheriff Sills, because I know where I was."