Six GBI agents were at the home investigating at the request of the Habersham County Sheriff's department, GBI spokesman John Bankhead said.
The preliminary investigation is looking at the case as a murder-suicide, but he did not have further details.
Schaefer, 73, was a Republican who represented a north Georgia district for two terms. She was a prominent conservative known as a vocal opponent of abortion and same-sex marriage.
State Rep. Rick Austin announced Schaefer's death to a packed House chamber Friday night and led lawmakers in a moment of silence.
"Nancy Schaefer was a great lady, and she served Georgia and her constituents with honor and grace," Austin, a Republican from Demorest, said.
State Sen. Don Thomas told The Atlanta Journal-Constitution he knew the couple well and that he believed Bruce Schaefer was suffering from cancer.
"In those moments, you are not at your complete sanity," said Thomas, a physician and Republican from Dalton. "Some people figure the best way is to end it for both of you. They were married for so long. Loved each other so much. When you see somebody that you love so much, every now and then, you think the best way out of it is to go and be with the Lord."
Schaefer moved to Turnerville after more than three decades in Atlanta, where she was a former candidate for mayor. She was also GOP nominee for lieutenant governor in 1994.
In 1986, Schaefer founded a nonprofit foundation, Family Concerns Inc., which focused on opposition to abortion and the display of the Ten Commandments in public buildings.