Nearly three years after receiving life in prison for the murders of three of actress and singer Jennifer Hudson’s relatives, William Balfour got another day in court today as his attorneys asked a state appeals panel to vacate the convictions.

“They’re putting it on him because they have nobody else,” Darrel F. Oman, an assistant appellate defender, said to 1st District Appellate Justices Michael B. Hyman, Aurelia Pucinski and Terrence J. Lavin.

Oman referenced trial testimony from a medical examiner which suggested Hudson’s 7-year-old nephew died during a window of time when Balfour was already in police custody.

Inside the car where Julian King’s body was found, investigators recovered several fingerprints and DNA traces that were complete enough to document but did not match Balfour, Oman said.

“They were extremely thorough in this case,” he said.

Oman also contended the missing car wasn’t found on the West Side until after Balfour was in custody.

Lavin asked Oman why the appeals panel should disregard some of the evidence presented to the jury while relying strongly on other evidence. He said the panel will consider the evidence shown to the jury in a light most favorable to the prosecution, and it could only overturn a verdict that was clearly unreasonable or ridiculous.

“You’re asking us to be inconsistent,” Lavin said.

“The evidence is simply not there,” Oman replied.

Lavin said the prosecution’s theory was “not a perfect ‘CSI’ case” and that both sides at trial made inferences which required the jurors to choose whom to believe.

Balfour, the ex-husband of Hudson’s sister, was found guilty in May 2012 of killing the singer’s mother, brother and nephew in an October 2008 home invasion at the family’s Englewood home.

Prosecutors argued Balfour became jealous that his estranged wife, Julia Hudson, was dating another man. After waiting for her to leave for work, prosecutors contended, he entered the house and shot Darnell Donerson and Jason Hudson.

Prosecutors alleged Balfour then drove off in Jason Hudson’s car, taking Julia Hudson’s son, Julian, with him.

After the two bodies were found inside the home, police issued an Amber Alert for Julian that included a description of his uncle’s SUV.

The vehicle was discovered three days later. Julian’s body was found in the back seat with a gunshot wound to the head.

A Cook County jury convicted Balfour on three counts of first-degree murder, one count of home invasion, one count residential burglary, one count aggravated kidnapping and one count of possession of a stolen vehicle.

Circuit Judge Charles P. Burns sentenced Balfour to two consecutive life sentences for the murders plus an additional 120 years for the other counts.

During appellate arguments today in the Bilandic Building, Balfour’s attorney argued the prosecution’s theory was undermined by its own evidence presented to the jury.

Oman said because the prosecution’s evidence showed Balfour could not have killed Julian, it therefore could not prove without a doubt he committed the other two murders.

“Somebody else is implicated in this case,” he said.

Oman contended that the shooting was a robbery related to Jason Hudson’s drug-dealing operation based from the house. Oman told the panel that Jason Hudson had previously been shot in an earlier home invasion related to drugs.

He then compared the case to that of Juan Rivera, who was convicted by Lake County juries three separate times for the 1992 rape and murder of an 11-year-old girl.

Prosecutors in each of Rivera’s trials relied on a confession that Rivera contended was false and coerced. In 2011, a 2nd District Appellate Court panel reversed the conviction, citing DNA evidence, and Rivera was released from prison.

At Balfour’s trial, the prosecution called 83 witnesses during 11 days of testimony at the Leighton Criminal Court Building.

The first witness was Jennifer Hudson, who was in Florida at the time of the murders but testified regarding the family’s strained relationship with Balfour.

Oman said the jury deliberated for three days and was split 9-3 on its final day. Because the case was so close, any error could have tipped the verdict against Balfour, he said.

In the state’s rebuttal, Cook County Assistant State’s Attorney Peter D. Fischer told the panel that everything Oman said was also told to the jury.

“Under that standard, the evidence is absolutely overwhelming,” Fischer said.

He said the lack of physical evidence linking Balfour to the scene is reasonably explained because a gunshot from a distance beyond 18 to 24 inches would not leave DNA on the victims, like a sexual assault or a stabbing would.

Prosecutors relied on testimony from an eyewitness who saw Balfour in a car from a window overlooking the street, he said.

The jury considered the caveats given the witness’ vantage point and still agreed with it. And no evidence physically excluded Balfour from being placed the car, Fischer said.

Hyman responded that the lack of physical evidence linking Balfour to the car raised a reasonable doubt.

Fischer also responded to Oman’s argument that the medical examiner’s time-of-death estimate proved Julian was killed after Balfour was already in custody.

“That isn’t really how it works,” Fischer said. “She didn’t say, ‘Seventy-two hours — boom — it’s over.’”

Rather, the examiner’s number was a general window that still fit the prosecution’s timeline, he said.

The oral arguments lasted about 90 minutes. The case is People v. William Balfour, No. 1-12-2325.