Johnson has accused Cosby of drugging and molesting her at a Los Angeles hotel bungalow in 1996.
Attorney Gloria Allred, who represents Johnson and many other accusers, said she hoped more can testify at the next trial.
The jury started deliberating Monday and first declared itself deadlocked Thursday on the three counts of aggravated indecent assault.
But the judge sent them back to try to reach a unanimous verdict.
He said Constand "is entitled to a verdict in this case and the citizens of Montgomery County, where this crime occurred, are entitled to a verdict in this case.
His mother, Betty Jackson, is an English fashion designer, and his father, David Cohen, who is French-Israeli, is his mother's business partner.
In Cosby's case, that could have involved the more than 60 other women who have accused him of assaults dating to the 1960s.
Duquesne University law professor Wes Oliver said that if Cosby had been convicted, those allegations could have compelled Judge Steven O'Neill to sentence him closer to 10 years.
Count 2 alleges she was unconscious or semi-conscious at the time and could not give consent.
Count 3 alleges all this happened after he gave her an intoxicant that substantially impaired her and stopped her from resisting.
Judge Steven O'Neill declared a mistrial after the jury of seven women and men — picked 482 kilometres away in the Pittsburgh area and sequestered since the trial began June 5 — announced they were hopelessly deadlocked after 52 hours of deliberations over six days.
In the statement, which Bill Cosby later tweeted, she attacked Judge O'Neill, describing him as "overtly arrogant" and accusing him of "collaborating with the district attorney." She described the prosecutor as "heinously and exploitively ambitious." Cosby listens to his wife Camille's statement being read aloud by Ebonee M.
Benson outside the Montgomery County Courthouse in Norristown, Pa., Saturday, June 17, 2017.
If he had been convicted, prosecutors say Cosby would have had to register as a sex offender and face an assessment to determine whether he was a sexually violent predator.