Spacey, 59, had been accused of groping an 18-year-old man in July 2016.
Spacey, who has won two Oscars, including the best actor Academy Award in 2000 for his role in "American Beauty", had pleaded not guilty to the charge.
The decision comes after the man accusing Spacey suddenly dropped his civil lawsuit against the Oscar victor.
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The two-time Oscar victor denies groping the man, whose mother - former Boston TV news anchor Heather Unruh - first went public with the allegations in 2017. The accuser's attorney claimed that his client lost the phone, but that they were able to retrieve data backed up on a computer.
"If you have a complaining witness who is allegedly a sexual assault victim, who is claiming the Fifth Amendment and is therefore is not going to testify, what have you got?"
He also testified that he had turned the phone back over to the accuser's family a few weeks after obtaining it. Spacey's defense, in turn, argued that the man deleted messages that could prove the actor's innocence. Spacey's attorneys alleged that the phone record had been edited, and the accuser's mother admitted to deleting some videos off the phone. He said on the stand that he had not been aware of that.
The young man and his family met with prosecutors Sunday and he decided not to waive his right to invoke the Fifth.
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The sexual allegations led Netflix to drop Spacey from the last season of "House of Cards" and resulted in his removal from Ridley Scott's 2017 movie "All the Money in the World".
Nantucket District Court Judge Thomas Barrett said at the time that he would give the accuser's attorney time to decide how to proceed. "He is the sole witness", he said.
In theory, prosecutors could have granted the accuser immunity for his testimony - but that would make a conviction virtually impossible with such a tainted witness.
Rapp's allegation caused the floodgates to burst as numerous other men accused Spacey of sexual misconduct, leading him to enter a treatment facility. The man said he fled when Spacey went to the bathroom.
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It's only his second quadruple-bogey in a major (he had one on the 11th hole in the final round of the 2013 U.S. Rory McIlroy has help looking for his ball after hitting into the long rough near the green on the first hole.