Balfour, 30, is the ex-husband of Hudson's sister, Julia. He is on trial for killing the three members of the sisters' family in 2008.
The Chicago Sun-Times said an hour-long video showing police interrogating Balfour the day of the slayings was shown to jurors Monday.
In the video, Balfour told the officers Jason Hudson, the brother of Jennifer and Julia, was a drug dealer who had a lot of enemies.
"It was a drug house. What do you expect?" he said, offering an explanation of why Jason and his mother, Darnell Donerson, might have been shot to death in their home.
The Sun-Times reported Balfour also demanded to see cellphone records police told him they had placing him at the scene of the crime. In addition, he denied having a weapon or knowing where Julia's 7-year-old son, Julian King, might be. The child was found dead three days later in Jason Hudson's stolen sport utility vehicle.
The newspaper said the jury could begin deliberations as early as Wednesday.