Although both he and his mother claim he had no part in the brutal slayings of Jennifer Hudson’s family last week, William ‘Flex’ Balfour will not take a lie detector test.

According to the AP, an anonymous police official says that Balfour was cooperating with police up until he was asked to take a polygraph test.

Balfour still has not been charged with the killings of Hudson’s mother, Darnell Donerson, 57, brother, Jason Hudson, 29, and nephew, Julian King, 7, who were all shot to death.

Yesterday a gun was found in some bushes in a vacant lot near where the white SUV was discovered. Police believe it may be the gun used in the murders.

The anonymous official told the AP that police do not believe anyone else was involved in the killings, despite reports stating otherwise.

The source added that someone else may have driven and dropped off the SUV, but that Balfour is “the only suspect in the killings (and there is) nothing to link a second individual” to the crime.

A police spokeswoman declined to comment on the official’s statements.

Balfour is a felon with a prior record of attempted murder, and was busted with cocaine last June.