Daniels was scheduled to appear at the Sirens strip club on Wednesday and Thursday nights, the club's website says.
The patron is not believed to have been detained.
The high-powered attorney claims the arrest was "part of a sting" based on a "puritan law" that says there is absolutely no touching in strip clubs in Columbus. In May, Trump said Daniels was paid to stop "false and extortionist accusations" she made about a sexual encounter with him. This was a setup & politically motivated. He later said Daniels is expected to be released on bail and charged with a misdemeanor for allowing touching. It reeks of desperation. "We will fight all bogus charges", Avenatti tweeted.
A man who answered the phone at Sirens early Thursday morning said, "We have no comment on that". He said his client was "performing the same performance that she has conducted at over a hundred strip clubs around the country".
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The Ohio strip club law prohibiting the touching of dancers, the Community Defense Act, was proposed by a Cincinnati-based conservative religious organization and approved in 2007.
Calls to the Columbus Police Department's media information officers went to voicemail.
Daniels, who claims to have had sex with President Donald Trump in 2006 when he was married, is suing the president and his former personal lawyer Michael Cohen over a nondisclosure agreement she signed to keep quiet on the alleged affair.
In April, Daniels filed suit in federal court in NY charging that Trump had defamed her.