The body of Julian King, 7, was discovered on Monday morning - three days after the star's mother and brother were found shot dead at the family home in Chicago.
The youngster's body had been left in a car parked about ten miles from the house.
Police Superintendent Jody Weis said post mortem results would determine how long the boy had been dead, but estimated the car had been abandoned for "a couple of days".
He added: "I suspect we'll have some evidence that will link us to the killer."
William Balfour, the boy's stepfather and estranged husband of Hudson's sister Julia, is being held in custody on a alleged parole violation. No-one has been charged over the deaths.