Marco McMillian's godfather, Carter Womack, said McMillian's family received the information from the Coahoma County coroner. Coroner Scotty Meredith declined to comment Monday, and a spokesman for the Coahoma County Sheriff's Department had no immediate comment.
But a person with direct knowledge of the investigation confirmed to The Associated Press that McMillian had some bruises and there were burns on at least one area of his body. The person wasn't authorized to publicly comment and spoke on condition of anonymity.
The cause of death has not been released. An autopsy was performed, but toxicology tests are pending, and authorities say it could take two weeks to get those results.
Womack said the coroner told family members that someone dragged McMillian's body under a fence and left it near a Mississippi River levee last week.
McMillian, 34, was a candidate for mayor of Clarksdale in the Mississippi Delta.
"We feel that this was not a random act of violence based on the condition of the body when it was found," said a statement released by his campaign.
The slaying received significant attention, in part, because McMillian's campaign said he was the first openly gay, viable candidate for public office in Mississippi.
Sheriff's deputies last week charged 22-year-old Lawrence Reed with murder in the case.
An investigation began Feb. 26 after McMillian's SUV slammed head-on into another vehicle on U.S. Highway 49 near the Coahoma and Tallahatchie county lines.
Reed was driving the car, but McMillian was not in it, authorities say. McMillian's body was found the next day.
Reed was treated for injuries at the Regional Medical Center in Memphis. The hospital said he was released Saturday. The Shelby County, Tenn., Sherriff's Office website showed Reed in custody Monday.