Mansfield police Lt. John Wendling would not say how the baby got the medication, which he said appears to be an anti-depressant.
"An autopsy was performed this morning to support our suspicions," Wendling said. "We have no reason to doubt that that (overdose) is the cause of death.
"The chances are better that it's going to be an aggravated murder than not. The elements are there to support aggravated murder. We surmise that from statements taken during this investigation."
Wendling declined to elaborate.
Redman pleaded innocent Friday. She was being held in the city jail on a $500,000 cash bond. While she was in jail, police served her with a misdemeanor warrant for failure to appear for arraignment. Defense attorney Terry Hitchman is representing her.
Wendling said Redman lives on Bartley Avenue with her two sons. Richland County Children Services took custody of them, he said.
Neighbor Sherry Carroll said the boys are 4 and 2. She added an older man and woman also live at the address. Redman is pregnant.
"It's just a sad situation," Carroll said. "It's awful."
Carroll said the children often were left unattended.
"I should have called Children Services a long time ago," she said. "Maybe they could have done something."
Wendling said the baby was taken to Akron two days before she died. He did not know the circumstances.
"Someone suggested the baby be taken to the hospital," Wendling said.
The case is the city's first homicide of the year.
"It's always sad when a baby dies, especially with the circumstances that have presented themselves," Wendling said. "It just seems like people don't think of alternative courses to take. It defies common sense.
"You try to understand what a person is thinking about. Every time you think you've got a grasp, something else happens to completely tear down that thought process.
"You just never know."
The veteran detective said the cases don't get any easier to take.
"You learn early in this job … never, ever think that you've seen everything, 'cause that's not in the cards," Wendling said.
Anyone with information on the case is asked to call Wendling at 419-755-9755 or Detective Jeff Shook at 419-774-3533.