Constand, 44, is the only one of dozens of Cosby accusers whose report led to a criminal trial because, in the other cases, the statute of limitations had expired.
Attorney Brian McMonagle spoke with Jean Casarez of CNN after jurors were deadlocked Saturday in the case near Philadelphia.
It's possible the next jury could be selected in another county so as not to place too heavy of a burden on Allegheny County, where Pittsburgh is located, said Dennis McAndrews, a former Philadelphia-area prosecutor.
McCloskey is the first of the jurors to speak out about the trial.
McCloskey posted his juror's badge on Facebook as proof of his role in the case.
The Associated Press does not typically identify people who say they are victims of sexual assault unless they grant permission, which Constand has done.
Jurors deliberated more than 52 hours over six days before telling a judge they couldn't break their deadlock.
Cosby, 79, had maintained his innocence even rejecting a friendly plea deal offered by prosecutors just before the trial started in early June.
Pennsylvania law allows the public release of jurors' identities, but judges have discretion to keep them a secret under certain conditions.
On Sunday's episode of Last Week Tonight, John Oliver briefly addressed the Bill Cosby trial and the recent announcement that the sexual assault case had ended in a mistrial. A hearing is scheduled for Tuesday. It's unclear how many jurors voted for conviction and how many wanted an acquittal. Cosby was performing there, and she says he invited her to a party where she accepted two pills from him. The court of public opinion has already reached their verdict and that comes from his own testimony.
"We get 12 people to agree on sex assault cases all the time, but this is not any case. It's an old case, it's a controversial case, it's a case that involves questions of consent", said Loyola Law School professor Laurie Levenson.
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Another one of Cosby's accusers, actor Kathy McKee, who alleges Cosby raped her in 1973, once described the incident - after which, she said, he pretended that nothing odd or remarkable had just happened between them - as an unthinkably violent encounter with hubris. His deposition testimony in her civil suit revealed that Cosby, someone who had a bestselling book about fatherhood, had procured Quaaludes for the sole reason of having sex with women who were not his wife. The defense had hoped, if it did, to introduce evidence she had previously dated a man.
"The key to retrying a case is to do it differently the second time, because the defense expects you to do it the same way", said Constand's lawyer, Dolores Troiani.
He remains free on $1 million bail.
Meanwhile, the judge has assured that he would try to schedule a new trial within 120 days.
Cosby is also battling sexual battery or defamation cases still pending by 10 women in California and MA. With the criminal case now set for a retrial, it appears that the MA civil case will be pushed back. Speaking in a calm and unemotional tone, Veronique Valliere, a psychologist, testified that sexual assault victims are frequently so traumatized that they can be confused about details.
For more on Cosby, including stories about the trial, historical photos, videos and an audio series exploring the case, visit http://www.apnews.com/tag/CosbyonTrial.
Kevin R. Steele, the district attorney for Montgomery County in Pennsylvania, has said he will seek a new trial against Bill Cosby.
The jury failed to reach a unanimous decision on any of the three counts against the comedian, ending the trial without a verdict after a long week of deliberations.
Women bringing civil cases would also likely find it easier to introduce testimony from other accusers to support claims that Cosby engaged in a pattern of assault, said Douglas Wigdor, a plaintiffs' attorney who represents clients in sexual harassment cases.