William Balfour, a “person of interest” in the slayings of Jennifer Hudson’s mother, brother and nephew, claims he had nothing to do with the murders, but refused to take a lie-detector test.

The estranged husband of Julia Hudson, the Academy Award winning actress’ sister, told police that he was in good terms with the Hudson family, but declined to undergo a polygraph examination and “stopped cooperating” the moment detectives asked him to do so, The Associated Press reported.

Although William Balfour has not been charged with the killings, he is being held in custody due to parole violation. He is on parole after spending several years behind bars for attempted murder, vehicular hijacking, as well as possessing a stolen vehicle, according to the Department of Corrections’ Web site.

Records even show that Balfour was detained by police in June for possession of cocaine, which police found in his car after stopping him for high speed driving.

On Wednesday, police discovered a handgun not far from the place where Jennifer Hudson’s 7-year-old nephew was found dead on Monday. The weapon matches the caliber of the gun that was used in the murder of Julian King, his grandmother, Darnell Donerson, and his uncle, Jason Hudson.

The gun was examined and proved to be a .45-caliber weapon and, in addition, the ammunition in it and the shell casings at the murder scenes were a match, the Chicago Tribune cited a law enforcement source as saying.

Along with the gun, which was discovered in thick shrubs, police reportedly collected “small bits” of evidence from the scene.

Now that another piece has found its place in the puzzle, authorities are resuming their searches and investigations in an attempt to solve the tragic mystery of the Hudson case.