John William Roche entered his plea during an appearance in federal court in Denver Tuesday. He faces up to five years in prison if convicted of leaving a profanity-laced threat on the 19-year-old woman's answering machine in July.
The case has led the 22-year-old Roche to withdraw from the University of Iowa. His friends say he's a sports fanatic and that he had been drinking all day at a golf tournament on the day the alleged threat was made.
Roche appeared before a federal magistrate who told him not to drink any alcohol and not travel outside of Colorado or Iowa. A November 3rd trial date has been set.
Roche said nothing in court and ignored reporters outside the courtroom.
Bryant is charged with sexually assaulting the resort employee near Vail on June 30. The Los Angeles Lakers star says the sex was consensual.