"I told him, 'I can't even talk, Mr. Cosby.' I started to panic," the former Temple University athletic department employee told police in 2005.
The statement was introduced at a preliminary hearing held to determine whether prosecutors have enough evidence to put the 78-year-old TV star on trial on sexual assault charges that could bring 10 years in prison.
In his own statement to police, also read in court, Cosby portrayed it as consensual sexual activity, saying Constand never said "no" as he put his hand down her pants.
Cosby's lawyers argued unsuccessfully that that would be hearsay and would deprive him of his right to confront his accuser.
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Such testimony from law enforcement officers is common practice at preliminary hearings in Pennsylvania, which have a far lower burden of proof than trials.
In her statement, Constand said Cosby penetrated her with his fingers as she drifted in and out of consciousness soon after he gave her the pills at his suburban Philadelphia mansion in 2004.
Constand said her legs felt "rubbery" and "like jelly." ''Everything was blurry and dizzy. I felt nauseous," she said. Constand told detectives that Cosby positioned himself behind her after telling her to lie down on the couch.
She said she awoke with her bra askew and did not remember undoing it.
In excerpts read in court from his own statement to police in 2005, a seemingly relaxed Cosby said he and Constand had had other "petting" sessions before.