Eugene Siller was shot in the head on Saturday on the green of the 10th hole at Pinetree Country Club in Kennesaw, near Atlanta, the Cobb County Police Department said.
Two other men were found shot dead in the bed of a white Ram 3500 pickup truck that was on the green, police said.
Police said Tuesday they believe Siller, 46, was shot because he was a witness who "happened upon a crime in progress involving the unknown suspect" and the two victims in the truck.
No arrests have been made but police said Tuesday they're following "active leads."
The victims in the truck don't appear to have any connection to the country club, police said. One of the men was the truck's owner, 76-year-old Paul Pierson of Kansas, and the second victim was identified Wednesday as 46-year-old Henry Valdez of California.
A motive isn't clear, police said.
Police added that they don't believe there's an active threat to the public. Anyone with information is asked to contact the police at 770-499-4111 or at email@example.com.