Police captured the parents — Donald Boyd Harris, 34, and Allison Studdard, 31 — early Thursday about 170 miles south of Atlanta in Sylvester, Ga.
Authorities said Thursday that Harris and Studdard were being held on felony drug warrants, and deputies would be headed to Georgia on Friday to bring them back to Mississippi.
Mississippi had issued an Amber Alert on Wednesday for the couple's 2-year-old daughter, Maliah Harris, after the parents fled with her. She was with them and unharmed when they were captured. Authorities released Maliah to the Georgia Department of Family and Children Services.
Coroner Greg Merchant in Lowndes County, Miss., said it could be weeks before toxicology results are available from Alyssa. He said an autopsy was completed Wednesday, but it did not reveal and cause or manner of death. He said the baby's body was being held in the Lowndes County morgue, and it will remain there until he talks to the girl's parents about funeral plans.
No charges had been filed in the baby's death, as of Thursday.
Ryan Rickert, chief investigator for the Lowndes County Sheriff's Department, said the couple and their two young daughters were living with Studdard's father, Roger Studdard, in his home in rural Caledonia, less than a mile from the Alabama state line.
Roger Studdard told investigators he woke to loud noises early Wednesday and found the couple trying to help their unresponsive baby, Rickert said. The investigator said the couple fled when Studdard called 911, and when deputies arrived, they found the baby's body in a basinet.
Rickert said investigators found methamphetamine in the home, but it did not appear anyone was manufacturing the drug there.
"It was a fairly clean home," Rickert said. "It is a nice single-family dwelling."
Harris and Allison Studdard did not have jobs outside the home, Rickert said. He said Harris worked on computers and refurbished cellphones at the home, and she assisted in that.
Rickert said he doesn't think the sheriff's department had ever been called to the home before Wednesday.
"We're still working on trying to pull records," Rickert said Thursday. "We never really had any contact with them, up until yesterday."
Harris has family ties in Georgia and an expired license there, according to the Mississippi Bureau of Investigation. The vehicle the couple was driving also had Georgia plates.
Police were holding Harris and Allison Studdard on felony warrants for possession of methamphetamine in Mississippi. Drugs also were found in the car, with additional charges possible, said Sylvester Police Chief Robert Jennings.
Studdard, who was driving, also faces a charge that the 2-year-old was not properly restrained in safety belts. Harris was charged with not wearing his safety belt, Jennings said.
Associated Press writers Jack Elliott Jr. in Jackson, Miss., and Jeff Martin in Atlanta contributed to this report.