It's the first time Cooper has answered questions about his wife's death and the couple's infidelity since her body was found July 14 in an undeveloped Cary subdivision.
In a videotaped deposition, Cooper tells lawyers about the events in the days and hours surrounding Nancy's disappearance and murder.
But in an affidavit filed Thursday, Cary Police Detective George Daniels says some of Cooper's statements in the video are inconsistent with statements made to police after Nancy's body was discovered.
He also says Cooper has not fully cooperated with the Cary Police Department in their investigation.
Cooper has not been named a suspect and he denies any involvement in the murder, but he's remained at the center of the murder investigation and a custody battle for the couple's two children.
Cary Police Chief Pat Bazemore will not speak to the specifics to the case, but in a statement Thursday says, "Detective Daniels has been able to meet the civil attorneys' requests for information without jeopardizing our murder investigation, which continues to be going very well and his sworn statement stands on its own and speaks for itself."
In the affidavit Detective Daniels doesn't say specifically which part of the interview does not match up.