Constand, who settled out of civil court with Cosby in 2005, alleges that Cosby gave her pills during an encounter at his home in 2004, which left her unable to stop his advances.
The prosecution rested its case on Friday after five days of testimony.
The trial is expected to run almost two weeks, with the defense launching their case in the next few days.
Jurors heard late Friday afternoon about Cosby's admission in his civil lawsuit deposition that he got at least seven quaalude prescriptions to give to women with whom he wanted to have consensual sex.
WHAT'S NEXT: Prosecutors are expected to use more of the deposition, including Cosby talking about giving quaaludes and alcohol to women he wanted to have sex with.
Cosby was all smiles as he walked out of court Friday, raising his wooden cane to salute well-wishers.
Cosby is charged with drugging and sexually assaulting Andrea Constand, a former administrator at Cosby's alma mater, Temple University, at his Philadelphia-area home in 2004. He contends the sexual encounter was consensual.
In the deposition, Cosby said he gave Constand three half-tablets of the cold and allergy medicine Benadryl.
Prosecutors have suggested he drugged her with something stronger, perhaps the quaaludes he admitted obtaining decades ago.
The mother of Andrea Constand, the woman he is accused of drugging and sexually assaulting, had called Cosby to ask about the allegations.
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"She said Cosby gave her pills he claimed were a natural remedy to ease her stress about a looming career change". He faces up to 10 years in prison if convicted. That information became public in 2015, when the revelations of the 2005 deposition were unsealed by a federal judge. Acting as an expert witness for the prosecution in the Bill Cosby trial, she testified about common post-sexual assault victim behavior.
Some 60 women have come forward to say Cosby sexually violated them, but the statute of limitations for prosecution had run out in almost every case.
"I'm apologizing because I'm thinking this is a dirty old man with a young girl".
Cosby testified at the time that he was anxious about his public image. Later, she added that he also said, "Oh I feel bad telling you this, it sounds perverted, do I sound like a perverted person?"
"Have you ever used this vehicle of an educational trust ... as a way of giving money to any other woman with whom you had a relationship?" he was asked in the deposition. Constand refused the offer and reported Cosby to police, filing suit after prosecutors failed to file charges.
Cosby accuser Andrea Constand waited a year to go to police. Cosby's attorney, Brian McMonagle, questioned Dr. Veronique Valliere about Facebook messages she made, apparently celebrating the fact that Cosby would be taken to trial.
O'Neill ruled the testimony permissible and rejected the request.
Benshoff says Constand testified that on a previous occasion, Cosby tried to unzip her trousers, but she rejected the advance and said, "I'm not here for that". Rohrig said the effects Constand described were consistent with the effects of Benadryl.
Andrew Wyatt told reporters during a lunch break on Friday that Cosby's team was still evaluating whether to have him take the stand.