While the 1 percent’s away, the cops will play.

Shocked cops in tiny East Hampton Village say they caught a couple of frisky fellow flatfoots trespassing in a cottage down the road from police headquarters — reportedly to have sex.

The two — she’s a 20-year-old part-time traffic-control officer, he’s a 31-year-old patrolman — were caught in a secluded, shingled hideaway, according to police in the scandalized station house.

The patrolman, who has not been named publicly, has been suspended with pay and relieved of his gun and badge, police said. He is believed to be out of the country.

The woman was summarily fired Friday at a village board meeting, retroactive to Dec. 30, the day of the ­alleged shenanigans.

She’s also a part-time maid — at the house where the alleged tryst occurred.

Both the maid and her patrolman-colleague were allegedly engaging in some off-duty internal investigations at the house on leafy Talmage Lane while the owner, prominent Manhattan interior designer J. Arthur Dunnam, 55, was away.

The two were allegedly caught when three house-guests arrived from Georgia, invited by Dunnam to stay for the New Year’s weekend, according to police paperwork obtained by The Post.

The three startled visitors quietly left and called in a trespass complaint to police, who were undoubtedly surprised by what, and whom, they found inside.

“Upon arrival, they located two suspects inside the residence that were not authorized to be there,” the East Hampton Village Police incident report states.

Dunnam declined to comment, but the incident report says “he does wish to pursue charges because no one should be in the house.”

Dunnam is design director of Jed Johnson Associates; his Sutton Place apartment has been featured in Architectural Digest.

The cops are being investigated for trespassing in the home for a “sexual encounter,” the East Hampton Star reported.

“Further departmental action is expected,” Chief of Police Gerard Larsen Jr. wrote — without a note of irony — in a press release.