The first time she witnessed a naked woman gyrating on the roof of a parking garage across from the federal jail in downtown Chicago, Briana Fitzgibbons couldn’t believe what she was seeing.

“I come from a town of 300 people in the middle of the fields in Minnesota, so it was weird, really weird,” says Fitzgibbons, a graduate student in Chicago at the time.

As Fitzgibbons watched from her high-rise apartment nearby and the woman on the top floor of the parking garage danced on that sultry September night, lights flickered off and on behind the narrow windows of the Metropolitan Correctional Center.

That’s how detainees held at the 27-story jail operated by the federal Bureau of Prisons across the street from the parking garage show their appreciation for the strippers who perform for them, people familiar with the performances told the Chicago Sun-Times.

They say the displays put on for those in the jail have gone on for years.

And they don’t always involve stripping, according to Fitzgibbons. Some days, the performances were strictly G-rated, she says. Once, a large group of what appeared to be family members — including children — gathered on the roof of the garage on Van Buren Street just west of Dearborn Street.

“They were there for hours, waving and taking pictures and everything,” Fitzgibbons says.

Another day, she says she was amazed to see two nude women on the roof who appeared to be performing sex acts for the inmates.

“My cousin from Minnesota was visiting me in October,” Fitzgibbons says. “She was very shocked, kind of like me. Most other people wouldn’t do this kind of thing for their boyfriend.”

Attorneys who represent clients held at the Metropolitan Correctional Center say they’ve seen the tawdry shows from their law offices in the nearby Monadnock Building. They’ve been going on for decades, one federal source says.

The detainees arrange the shows to prove they’re the top dogs in the jail, another source says. Often, the women will flash money — as well as skin — to show how rich and powerful their boyfriends are, he says.

It doesn’t appear that anyone has been arrested in connection with the jailhouse strip club.

Prison authorities say they can’t do anything about what’s going on at the parking garage.

Asked about the performances, a spokesman for the federal Bureau of Prisons, which runs the jail, says: “We are aware of the situation and have notified the owner of the property, but because it is private property, the Bureau of Prisons has no authority to remove people from the property.”

An executive for the company that runs the garage says he doesn’t know anything about the nude displays. A security guard was stationed atop the garage this past week, though.

Thaddeus “T.J.” Jimenez, a well-known Chicago gang leader who was held at the federal jail downtown, says some of the garage-top shows were for him.

In a brief interview, Jimenez says he didn’t pay for the dances. A woman stripping on the roof for him was simply “showing her love,” according to Jimenez, who says she sometimes would stand on the roof of the garage holding a sign that said “Free T.J.”

Jimenez won $25 million from the city of Chicago in 2012 in a wrongful-conviction lawsuit, then showered millions of his winnings on expanding his gang, the Sun-Times has reported.

He was sentenced in March to more than nine years in federal prison for possession of a gun he used to shoot a man in the legs in August 2015 on the city’s Northwest Side. He faces separate charges in Cook County criminal court for the shooting itself and is no longer being held at the MCC. Instead, because Cook County officials decided his stature as a gang leader might cause problems at the Cook County Jail, he is being held at the Kendall County Jail while awaiting trial.

Jimenez’s lawyer declined to comment. So did a spokesman for the U.S. attorney’s office.

Almost five years ago, authorities had to deal with another embarrassing situation involving the federal jail in downtown Chicago. In 2012, the jail got national attention after two convicted bank robbers fashioned a rope from bedsheets, escaped through a hole they carved out of the window slot of their 17th-floor cell and rappelled to freedom.

Within weeks, both men were recaptured in the Chicago area.