Evans handed him the girl after Oliver said they needed to go to the station and talk, and then sped away, the chief said.
"What could have been a day of great tragedy has really been a day of joy", Tecklenburg said.
Four-year-old Heidi Todd from Johns Island was reported missing on February 13.
A girl who was reportedly kidnapped from SC has been found safe and sound in St. Clair County, according to Riverside Mayor Rusty Jessup. When the officer obliged, the sleeping man woke up and drove off. The authorities there attempted to get hold of him, but he fled.
The driver remains at large after fleeing the scene in a blue sedan with an IL tag.
She was taken from her home Tuesday night after her mother was badly beaten in an attack.
"She is in the hospital. She is considered medical to be in fair condition", Mayor Tecklenburg told reporters Wednesday afternoon.More news: Commonwealth Games place with Team Scotland for Adam Hall
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Oliver said he and the fire chief found a man sleeping inside a vehicle with 4-year-old Heidi Todd inside.
He said the girl's father was out of town on a Coast Guard training mission when Todd vanished.
Agents with the Federal Bureau of Investigation, the South Carolina Law Enforcement Division and the Department of Natural Resources are also assisting Charleston Police and Fire officials as well as rescue teams.
Earlier Wednesday morning, the South Carolina Law Enforcement Division issued a statewide alert for the 4-year-old girl. They were not able to issue an Amber Alert because there was a lack of information on a possible suspect.
The mayor said he had visited with the Todds at the hospital, and he described them as a wonderful family. Officials said Evans was prior armed robbery and second-degree burglary convictions. He is described as a slender Hispanic man, 24 to 30 years old, with short dark hair and a tattoo of a flame on one side of his face, a tattoo of a lightning bolt on the other.
Anyone who spots Heidi should call 911 immediately.
Interim Police Chief Jerome Taylor with the Charleston Police Department says they are trying to "unravel" a motive.