Bibb County Coroner Leon Jones says a body was found Saturday morning at 3565 Case Street.
The victim is 30-year-old LaSmockie Fountain. She was found after an apparent domestic dispute with one gunshot wound to the head.
Her grandmother says she heard two shots fired around 5:30 a.m. She found Fountain shortly after.
Lt. Randy Gonzalez says Fountain had just returned to Macon from out of town and was staying with a relative.
Investigators are looking for 38-year-old Derrick Khunta Booze in connection with Fountain's death. He is 38 years old. Booze also has active warrants for Aggravated Assault/Family Violence, Possession of a Firearm by a Convicted Felon, Home Invasion and Pointing a Pistol at Another.
Anyone with information on the case can call Macon Regional Crimestoppers at 1-877-68-CRIME.