The reality TV star and former supermodel, who would have been 27 at the time, said Cosby called her to his show in Lake Tahoe, where he said they could discuss work and her singing career.
"When I arrived in Lake Tahoe, Bill was performing at the venue," Dickinson told ET. "And then after dinner in my room, he'd given me wine and a pill. The next morning I woke up and I wasn't wearing my pajamas. And I remembered before I passed out that I had been sexually assaulted by this man."
"Before I woke up in the morning, the last thing I remember was Bill Cosby in a patchwork robe, dropping his robe and getting on top of me," she added. "And I remember a lot of pain. The next morning I remember waking up with my pajamas off and there was semen in between my legs."
Dickinson, 59, is the latest woman to come forward with allegations of sexual assault against Cosby, who said in a statement via his lawyer on Sunday that he "does not intend to dignify" allegations he described as "decade-old" and "discredited."
On Monday, music industry publicist Joan Tarshis said Cosby drugged and assaulted her twice in 1969, when she was 19.
Prior to Tarshis, only two women, Barbara Bowman and Tamara Green, have publicly accused the 77-year-old comedian of sexual assault. There are reportedly another 11 women who settled out of court and have not gone public with their story.
Dickinson said she wrote about the alleged incident in her 2002 autobiography, No Lifeguard on Duty: The Accidental Life of the World's First Supermodel, but Cosby's lawyers pressured her publisher to cut the passage.
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She said she is speaking out now because "It's the right thing to do, and it happened to me, and this is the true story."
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