Mr Adams has been questioned at Antrim PSNI Station since Wednesday, after he was arrested in connection with the murder of Jean McConville.
The 37-year-old widow and mother of 10 was abducted from her home in west Belfast, shot and secretly buried by the IRA.
Her body was found a beach in County Louth in 2003.
Mr Adams has always denied involvement in the killing.
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What does it mean: file sent to Public Prosecution Service? Any UK readers?