Daniels, whose real name is Stephanie Clifford, was arrested and charged in the early hours of Thursday after being accused of touching three customers, who turned out to be undercover detectives, police in the city of Columbus say.

The charges were dropped hours later with Columbus City Attorney Zach Klein saying Daniels had not committed a crime because she did not perform regularly at the club, as required under the law.

Columbus Police Chief Kim Jacobs said officers at the club missed that element of the law.

"The facts behind the charges and the behaviour witnessed by the vice officers are a matter of record, and the officers were well within their area of responsibility when taking enforcement action," Jacobs said in a statement.

"Nevertheless, a mistake was made and I accept full responsibility."

Jacobs said the police department will now review the officers' motivation "to ensure that our core values and duty to serve our community to the best of our ability continue to be the basis for our actions."

But Daniels' lawyer, Michael Avenatti, has tweeted that he believes the arrest was a set up and politically motivated.

Avenatti is seeking an open investigation into the officers' conduct including an examination of their social media accounts.

"Certain of these accounts appear to have been very pro-Trump. In the event it is discovered that my client was targeted & arrested because of our opposition to Mr. Trump, the resulting lawsuit & action will be swift and devastating," he tweeted on Thursday.

Police earlier said Daniels and two other dancers were arrested at the Sirens Gentlemen's Club as part of an investigation into alleged human trafficking, prostitution and other crimes at adult entertainment clubs in the city.

According to an arrest affidavit cited by the New York Times, Daniels was dancing topless at the club when she pressed patrons' faces into her chest, fondled the breasts of some women in the audience and performed similar acts on three police officers who were at the establishment.

Daniels has filed two civil lawsuits against Trump, with whom she said she had a sexual encounter in 2006, a decade before he was elected president.

One lawsuit seeks to get out of a non-disclosure agreement she signed the month before the 2016 election in exchange for $US130,000 to keep the episode secret, while the other is for defamation. Trump has denied the affair.

Australian Associated Press