The Madison County Sheriff's Office said in a press release Sunday that the dead were James Clark Jackson, 55; Karen Lee Jackson, 53; and Chante Latrice Davis, 26. Sheriff's officials have not elaborated beyond the press release, which did not say how the three were related.
However, Robert Anthony, who said he was a relative of those killed, told WVIR-TV that a husband, wife and their child had died.
Their deaths are being investigated as homicides, and all three had trauma to their upper bodies.
Deputies were first called to the home about 90 miles southwest of Washington, D.C., on Saturday morning when the man was found in his yard. The other two were found inside the home.
A pickup truck had been taken from the home, which officials said was a copper 2005 Chevrolet Colorado extended cab.
Anthony told the television station that he had come to the scene to console family members.
"This is a terrible tragedy," he said. "A husband and wife and one of the children have left us, and we don't have all of the pieces to the puzzle."