The dispute over the slur postponed Williams' retrial on reckless manslaughter, which was to have begun in January.
Williams, 40, was convicted in April 2004 on four counts stemming from a failed attempt to cover up the 2002 shooting of hired driver Costas Christofi, 55.
A jury acquitted Williams of aggravated manslaughter but deadlocked on the reckless manslaughter count. He has been free on bail since the shooting.
A three-judge panel was scheduled to hear attorneys' arguments Wednesday morning.
Williams' attorneys have argued that prosecutors must give them all details about the slur, including the identities of the officer who made it and the person who overheard it and subsequently filed an official complaint.
The unidentified officer did not testify at the first trial and has since resigned from the prosecutor's office.
Hunterdon County Prosecutor J. Patrick Barnes alerted State Superior Court Judge Edward M. Coleman about the unspecified slur in October, telling him that a "superior officer" was accused of using a racial epithet to describe Williams in a meeting sometime before the 2004 trial.
Prosecutors have denied that they acted improperly by failing to notify the defense team in 2004 about the incident or the resulting investigation.
