Sharon Hunt's killer must be found, said Larry "Kite" Johnson, a Leflore County supervisor.
Hunt was murdered Dec. 2 as she exited her home at 215 E. McLaurin St.
Authorities have yet to arrest anyone in the week-old shooting death.
"We're following up on leads, but we don't have any arrests," said Greenwood Assistant Police Chief Henry Purnell on Friday.
A check of the docket late Saturday showed no arrests in connection with the murder.
Hunt's family buried her body Saturday afternoon.
The 39-year-old mother was the second person killed within 24 hours in the McLaurin Street area.
Johnson's nephew, Johnathan "John-John" McCoy, 19, was shot to death Dec. 1 at the intersection of Roosevelt and McLaurin streets shortly after noon.
Hunt's son, Rordera Hunt, 16, was arrested and accused of killing McCoy.
But Johnson said the family still wants to know who might have killed Rordera's mother, even if the investigation reaches into the Johnson-McCoy family.
"There's still another one out there, and that person needs to be brought to justice," Johnson said.
The supervisor and his family have offered to put up $2,000 for information leading to the arrest and conviction of killers in both cases.
"We also encourage the city to get a tipster line started," Johnson said.
Last week, the Greenwood City Council approved creation of a Crime Stoppers program, which allows payment for anonymous tipster information in various cases.
