The 72-year-old producer was taken to jail, where he was booked for investigation of felony domestic violence, Park said. He was released on $50,000 bail and ordered to appear in court next month.
Park said he did not know whom Cornelius was suspected of assaulting.
A call to Cornelius' production office was not immediately returned.
Cornelius started "Soul Train" in 1970 to showcase black music and culture, introducing television audiences to such legendary artists as Aretha Franklin, Marvin Gaye and Barry White. The series spawned a franchise that includes the Soul Train Music Awards, the Soul Train Lady of Soul Awards and the Soul Train Christmas Starfest.
Cornelius stepped down as "Soul Train" host in 1993.