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Deputies said they spotted Kayla Morgan walking with the infant on State Road 40.
Investigators said a deputy tried to speak with Morgan, but she ran away, narrowly missing vehicles.
Morgan walked across the road in a zig-zag pattern while carrying the child "as if she (were) carrying a jacket draped over her right arm, allowing the victim to flail," an arrest report said.
She hid behind vehicles, sprinted and "deliberately dropped the victim head first" on the side of the road, the report said.
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The deputy shocked Morgan with a Taser twice and arrested her, officials said. They said she was grunting and making other abnormal sounds.
The deputy sat Morgan in her patrol car and asked her what her name is, to which she replied with an expletive.
"She advised she believed I was a monster trying to suck her blood," the deputy wrote in the report.
Investigators said the boy's skull was fractured from being thrown to the ground.
A worker at an apartment complex where Morgan lives told WFTV that she moved there about two months ago and that the infant is about 6 weeks old.
Morgan is being held without bail at the Marion County Jail on charges of aggravated child abuse and resisting an officer without violence.
The case is being investigated by the Florida Department of Children and Families.