Whitlow said the family moved in December to an apartment in New Albany, an Indiana city less than a mile north of Louisville, Ky.
The mother and children's bodies were found Wednesday. Floyd County Coroner Leslie Knable said autopsies were performed Thursday and she plans to release details concerning the deaths on Friday.
Police said further testing is needed to determine the exact cause of the deaths. Knable said there were no visible injuries.
Whitlow did not immediately respond to messages Thursday from The Associated Press, but he has said that investigators are treating the deaths as homicides despite the lack of any obvious signs of foul play. Investigators have not identified any suspects.
A person walking through Binford Park in New Albany spotted the bodies in Falling Run Creek on Wednesday evening, Whitlow said. The creek is 12 to 18 inches deep. Whitlow did not have an estimate of how long the bodies had been in the creek.
WHAS-TV reported no vehicles were found near the bodies.
It's been nine years since a body was found in Binford Park, located in the center of the city.
"We haven't had many ones like this, especially with children," Whitlow told the News and Tribune.