Jones is jailed on $500,000 bail. The baby girl's body has been transported to the MS state crime lab for autopsy.
Authorities say she was found inside the home by a relative on Monday night. Williams says autopsy results weren't yet complete Tuesday afternoon. Police in turn called the sheriff's office and others for assistance.
Williams said the grandmother's brother found the body Monday night and called police in Shaw, a tow of about 2,000 people approximately 100 miles (160 kilometers) northwest of Jackson. Authorities say she had been living with her grandmother at the time of death.
"I have been in law enforcement a long time and one of the hardest things that I have experienced is when you see a child as a victim", Williams told reporters. The grandmother was taken in for questioning but has not yet been named or formally charged with a crime, according to the Associated Press.
'When deputies arrived on the scene, it was confirmed that a homicide had taken place inside the home, ' Williams said at a press conference broadcast by WREG.
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"Again, we might get some closure once we sit down with the investigator and once they present that to a judge for official charges", he said.
Mitchell didn't immediately return a phone call and an email seeking comment Tuesday. Williams said those toys had belonged to the child. "I mean, if they didn't want her why keep her?" said neighbor Tomorrow Williams.
A woman in Greenville, about 20 miles from Shaw, pleaded guilty to killing her 3-year-old son in an oven in March 2011.
Robinson pleaded guilty to the murder and received a sentence of life in prison.