Williams, according to the report, was pulled over around 11:30 p.m. on June 18, 2011, by Arkansas police for crossing the center line.
Williams reportedly registered a .10 on the BAC test, which is over the legal limit of .08 limit. Williams was then arrested, charged and eventually released, according to the report.
"Corey did not report this incident to us when it happened due to the prohibition of contact during last year's work stoppage," the Lions said in a statement published by the Detroit Free-Press. "We are aware of today's reports. We are in the process of gathering more information and will have further comment when appropriate."
Rickey Hicks, Williams' attorney, filed a motion to the court claiming Williams did not cross the center line and was racially profiled, further stating that Williams and all other passengers were African-American.
Hicks said Williams "was driving a Ford F650, which is an unusually large Ford pick-up truck, with unusually large wheels and tires," according to the report.
Monticello District Judge Ken Harper is expected to rule within a week after taking the case "under advisement."
Williams had 31 tackles and two sacks last season, his second with the Lions and eighth overall in the NFL.