More charges are expected to be filed in the case, authorities said.
Terry reported the boy missing on Sunday, but investigators became suspicious after she changed her story about how the child disappeared while taking with police Monday.
Monday night, a body of a toddler matching Emilliano's description was found at a waste collection site in Bedford. After the discovery of the body, police obtained two search warrants - one for Terry's apartment and the other for her DNA.
Trying to Find a Motive
The DNA will be used to positively identify the body. The cause of Emilliano's death has yet to be determined.
Cuyahoga County Deputy Chief Edward Tomba said investigators have not been able to locate anyone who saw the child alive since the night before Thanksgiving.
Tomba said investigators were looking at online postings by Terry to try to determine a motive.
A spokesperson for Children and Family Services said the family has a long history of interaction with the agency. Terry's 5-year-old and 5-month-old sons are now with a foster family.
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