New Albany police Maj. Keith Whitlow said autopsies were performed on the bodies of Jamie Clutter, 35, Brandon Clutter, 10, and Katelyn Clutter, 6 months, at the Kentucky Medical Examiner's office in Louisville, Ky.
Further tests were being conducted to determine how each of the victims died, he said..
Police found the bodies in Falling Run Creek in the park about 5:15 p.m. Wednesday, the News and Tribune, Jeffersonville, Ind., reported.
Whitlow said the police department was conducting a "homicide investigation" but no suspects had been identified.
He did say the victims were the first bodies found in Binford Park in nine years.
"We haven't had many ones like this, especially with children," Whitlow said.
The newspaper said the victims had moved from the state of Washington to an apartment in New Albany in December.