Until Monday, police had publicly identified Balfour only as a "person of interest" in the investigation. He had not been charged as of Monday night, said Tandra Simonton, a spokeswoman for the Cook County state's attorney's office.
Balfour's attorney said his client told him he is innocent.
"He vehemently denies that he is guilty in this case," Joshua Kutnick told reporters outside police headquarters. "Any evidence pointing to Mr. Balfour is not even thin. It is very, very weak."
The bodies of Jennifer Hudson's mother, Darnell Hudson Donerson, and brother, Jason Hudson, were discovered Oct. 24 at the family's home on the South Side of Chicago. The body of 7-year-old Julian King was found three days later in a sport utility vehicle on the West Side. All three had been shot.
Police took Balfour into custody the same day the bodies of Donerson and Hudson were discovered. After 48 hours - the longest Chicago police can hold a person without charges - Balfour was taken by the Illinois Department of Corrections on the suspected parole violation.
Balfour - Julian's stepfather and the estranged husband of Jennifer Hudson's older sister, Julia Hudson - served seven years for a 1999 attempted murder and vehicular hijacking conviction.
Balfour had refused to take a lie-detector test and stopped cooperating with detectives, according to a police official who was not authorized to discuss the case publicly and spoke on condition of anonymity.
Police have confirmed they found the gun used in the killings. The .45-caliber gun was discovered Oct. 29 in a vacant lot in the West Side neighborhood where King's body was found a few days earlier.
The police spokeswoman declined to discuss any evidence Monday. But after a hearing at the prison last month, the chairman of the Illinois Prisoner Review Board said a woman had told authorities that a gun used in the slayings was "identical" to the gun that was recovered.
At the time, board Chairman Jorge Montes said the evidence was key to a decision finding probable cause that Balfour violated his parole and should remain locked up pending a Dec. 3 hearing before a review board panel.
Balfour's mother told reporters outside the police station Monday night that authorities don't have a case against her son.
"If they found gun powder on his hands, you got a case; if they found a gun on him, he had a case; if they found a fingerprint on the truck that he did this, you got a case; but they don't have nothing," Michelle Davis-Balfour said.
Jennifer Hudson was a finalist in the 2004 season of "American Idol" and won her Oscar in 2007 for her film debut, a supporting role in "Dreamgirls." She has mostly stayed out of the spotlight and close to her family since the killings.
Her personal publicist, Lisa Kasteler, declined comment on Monday.
Associated Press writers Sophia Tareen and Caryn Rousseau in Chicago and AP Music Writer Nekesa Mumbi Moody in Miami contributed to this report.