The 80-year-old comedy legend has been charged with three counts of aggravated indecent assault.
But Dickinson is one of five "prior bad acts" witnesses, who have been permitted to testify.
The prosecution is arguing the "prior bad acts" witnesses demonstrate a pattern of behaviour in Cosby which is consistent with Constand's claims against him.
Dickinson testified that she had hoped to pursue a career as a singer and Cosby flew her to Lake Tahoe, an alpine lake resort town which straddles California and Nevada, to meet with a vocal coach.
After dinner with Cosby and another man, Dickinson said she told Cosby she was suffering from menstrual cramps.
Cosby offered her what appeared to be pain medication but Dickinson said she later became light-headed at which point Cosby "got on top of her".
"He smelled like cigars and espresso and his body odour," Dickinson said. "I couldn't move, I felt like I was rendered motionless, just immobile.
"I was thinking, what the heck, what the heck is he doing? I was just in shock. I didn't consent to this. I hadn't said yes.
"Here was America's dad on top of me, [a] happily married man with five children and how very wrong it was."
Dickinson told the court she felt vaginal pain and "passed out after he entered me."
"It was gross," Dickinson said.
Dickinson then clashed with Cosby's defence attorney Tom Mesereau during his cross-examination, in an exchange which US media outlets described as "heated".
Mesereau challenged Dickinson's court testimony, noting that in her 2002 biography No Lifeguard on Duty the Lake Tahoe story ended without any suggestion of misbehaviour on Cosby's part.
"You tell a completely different story in the book, right?" Mesereau asked her.
Dickinson then said the account in her biogaphy was false.
"Its all a fabrication there," Dickinson said, referring to the book. "I wanted the pay cheque from the book."
Mesereau responded: "So you made things up to get a pay cheque?"
Dickinson told the court her publisher was aware of the sexual assault but they had recommended she remove it to avoid potential litigation.
During the 1970s and 1980s Dickinson was one of America's most successful models, and was represented by two iconic agencies Ford Models and, later, Elite Model Management.
She appeared frequently on the cover of magazines such as Vogue, Harper's Bazaar and Cosmopolitan and was associated with a number of high-profile beauty and fashion brands including Revlon, Christian Dior and Max Factor.
In 2003, Dickinson returned to prominence as one of the judges on America's Next Top Model; she later fronted her own reality show, The Janice Dickinson Modeling Agency, and appeared on I'm a Celebrity … Get Me out of Here.
Dickinson was the fourth of five "prior bad acts" witnesses to testify in the case; Janice Baker-Kinney, Heidi Thomas and Chelan Lasha detailed similar incidents in 1982, 1984 and 1986.
Mesereau described the "prior bad acts" strategy as "prosecution by distraction".
Michael Idato is a Senior Writer based in Los Angeles for The Sydney Morning Herald.
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