Civilians Mustapha Jabbi, Saikuba Jabbi and sub-inspector Fakebba Jawara of The Gambia Police Force were arrested on Friday and charged with treason and conspiracy to commit a felony.
They were remanded in custody at the Mile 2 Prison in the capital Banjul.
Last month, the government said it had foiled a coup attempt and detained some military personnel.
Officials have arrested at least seven soldiers, including a captain and lieutenant.
Opposition politician Momodou Sabally, a former minister of presidential affairs under ex-leader Yahya Jammeh, was arrested and later released.
Last week, the West African nation set up an "investigative panel" to probe the alleged coup with 30 days to complete its work.
On Thursday, in a first revelation of details of the coup attempt, national security adviser Abubakarr Suleiman Jeng said the plotters aimed to "arrest cabinet ministers and senior government officials to use them as hostages to prevent any foreign intervention.''
"They also had plans to retire all senior military officers from the rank of major and above and restructure (the army)," he told reporters in the capital, Banjul.
The Gambia, a fragile democracy is still scarred by a brutal 22-year dictatorship under former leader Jammeh.