Five progressive members of the City Council showed up at a Brooklyn jail early Thursday morning to bail out an inmate — only to be turned away over a paperwork snafu.

The pols — Stephen Levin, Antonio Reynoso, Jumaane Williams, Alicka Ampry-Samuel and Brad Lander, all members of the Progressive Caucus — showed up at the Brooklyn Detention Complex on Atlantic Avenue with a $3,500 check.

“We are members of the New York City Council,” Lander, who represents Park Slope section of Brooklyn and nearby areas, told the clerk.

But the woman behind the window informed them that the female defendant was “in transit” – and couldn’t be formally bailed out until she was taken to Rikers Island later in the day.

“We can’t post the bail because this woman is in transit,” Lander told a throng of reporters and photographers who were on hand.

The pols could’ve put up cash to get the woman sprung from court, but opted to have Progressive Caucus Director Zara Naris return later in the afternoon with the check.

The Council members declined to provide the inmate’s name or details about her offense.

A lawyer for RFK claimed the woman had been brought to court in error.

“She doesn’t have a court date,” RFK lawyer Amanda Jack said, declining to provide details to back up the assertion.

The woman at the bail window told The Post she never told RFK or the councilmembers that the defendant was moved in error. The Department of Correction said it received an order from the Office of Court Administration to move the defendant, and DOC followed the instructions.

“No one was accidentally taken to court today. We received an order to present this inmate at court today and we did. Bail processing cannot begin until the inmate’s court appearance is over, as the disposition of their case can change,” a DOC spokesman said.

The woman had been selected for a bailout by the Robert F. Kennedy Human Rights initiative, a charity that plans to spend $5 million to free hundreds of female and teenage defendants from behind bars.