At last year's trial, Cosby's lawyers suggested that Constand and the former "Cosby Show" star were lovers who'd been intimate with each other in the past.
Ms Jackson's testimony was blocked by a judge at last year's initial trial after Ms Constand denied knowing her.
Constand was the director of women's basketball operations at Temple University in Philadelphia when she met Cosby, a powerful alumnus and member of the board of trustees.
The ruling by Judge Steven T. O'Neill gave the prosecution a key victory in its effort to portray Cosby as a serial sexual predator. And she said her phone calls to Cosby were about basketball and had nothing to do with romance. They argued to the court, the statements are irrelevant because there is no evidence Cosby gave Constand the now-banned drug.
Constand says Cosby knocked her out with the pills and then sexually assaulted her.
What may be different this time around is that the jury has heard from a total of five women who have told very similar stories on the witness stand about being courted by Cosby and being furnished with drugs and alcohol before drifting in and out of consciousness and raped.
A spokeswoman for the 80-year-old comedian blasted his chief accuser and her mother as they arrived at a suburban Philadelphia courthouse Tuesday morning.
He said Constand didn't appear affected by the medicine while they were, in his words, consensually "petting". Cosby lawyer Tom Mesereau asked her.
Constand, who's from the Toronto area, told Mesereau she was just being nice when she hugged Cosby or kissed him on the cheek, because she was grateful for his friendship and mentorship. "And I don't feel her say anything", he said in the deposition. "This isn't about money".
She remained outwardly calm during two hours of cross-examination in the sexual assault retrial, fending off queries on topics that the defence brought forward to indicate she had converted a consensual sexual encounter with Cosby into a criminal assault in order to score a big payday.
Following Constand's testimony Monday, her mother, Gianna Constand, took the witness stand.
Constand testified she had taken blue pills from Cosby, and when Constand's mother questioned Cosby about the pills, he said they were prescription pills.
"I trusted him because he's 'America's Dad, '" Lublin said. He says she showed no ill effects from the pills and did not object when he touched her. Her testimony prompted Cosby, sitting with his lawyers at the defense table, to open his eyes wide.
Cosby said at a deposition related to Ms Constand's lawsuit against him that he had got quaaludes from his doctor in Los Angeles in the 1970s.
The first criminal trial ended with the jury unable to reach a verdict.
Under questioning from both the prosecution and defense, Constand denied staying with any other employees during road trips. His defense team has called Constand a "con artist" who set him up by leveling false accusations of sexual assault. He also questioned her about her various phone calls to Cosby in the days after she was assaulted and laid special stress on the fact she called Cosby twice on Valentine's Day.
A former reality TV personality who has called herself the "world's first supermodel", Dickinson became one of the first women to go public with her allegations against Cosby when she told her story on "Entertainment Tonight" in 2014. She said she knew of Jackson's name but had no relationship with her. Williams started 10in10Biz, an alleged pyramid scheme Constand sent emails about while working at Temple.
On Monday, Constand testified she did not "recall ever having a conversation with" Jackson.
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