According to the Madison PD, the woman claims the incident went down after the rapper — real name Joseph Cartagena – performed at a concert at The Orpheum Theater last night.

Cops say the woman claims, “shortly after the concert had concluded … [the woman] found herself inside of a Cadillac Limousine with Joseph Cartagena and other male subjects all with the destination of a hotel located on Madison’s west side.”

Cops tell TMZ Fat Joe was detained for questioning — but he was not arrested. He was released this morning — sometime before 7 AM.

So far, no arrests have been made and police tell us the investigation is ongoing.

Today, Joe’s lawyer Dawn Florio released this statement:

Rapper Joseph Cartagena, known as Fat Joe, members of his entourage and security staff were briefly questioned by members of the Madison, Wisconsin Police Department who were investigating false allegations made by a woman who initially posed as a fan and later claimed to be the victim of an assault after demanding money.

At no point did Mr. Cartagena or any member of his entourage assault or have any improper contact with the woman. It is truly unfortunate that false allegations such as these cause the public to doubt the claims of actual victims of sexual assaults.