Cosby, 80, is charged with drugging and molesting Constand, a former employee of Temple University's basketball programme, at his suburban Philadelphia home in 2004.
Constand says he gave her pills that made her woozy, and then penetrated her with his fingers as she lay incapacitated, unable to tell him to stop.
Cosby's first trial last year ended with the jury hopelessly deadlocked. His retrial is expected to last a month.
Cosby faces three counts of aggravated indecent assault, each punishable by up to 10 years in prison.
Ahead of opening statements, a topless protester, who had appeared on several episodes of The Cosby Show as a child, jumped a barricade and got within metres of Cosby as the comedian entered the courthouse.
The woman, whose body was scrawled with the names of more than 50 Cosby accusers as well as the words "Women's Lives Matter", ran in front of Cosby and toward a bank of TV cameras but was intercepted by sheriff's deputies and led away in handcuffs.
The protester, Nicolle Rochelle, 39, of Little Falls, New Jersey, was charged with disorderly conduct and released.
"The main goal was to make Cosby uncomfortable because that is exactly what he has been doing for decades to women," Rochelle, a member of the European feminist group Femen, said afterward.
- AP
