Former Alabama Senate candidate Moore claims he was defamed and that he was tricked into appearing on the satirical show.
Cohen invited former U.S. Senate candidate from Alabama Roy Moore under the pretense of granting him an award for his support for Israel, but he used the opportunity to mock and embarrass the Republican.
Lawyers for the Republican judge and his wife claimed that Cohen "falsely painted, portrayed, mocked and with malice defamed Judge Moore as a sex offender, which he is not".
The Republican judge, who lost his bid for Senate past year after being accused of initiating sexual relationships with teenagers while in his 30s, filed the lawsuit Wednesday in the D.C. District Court. He has denied the misconduct allegations.
In legal documents filed in Washington DC, Mr Moore accused Cohen of portraying him as a sex offender. When Cohen waved the wand over Moore, it beeped loudly.
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Nancy Pelosi, the House Minority Leader, said that "the president saying it is treason is a manifestation of his instability". The staffer says that Trump is unpredictable, amoral, and a danger to the health of the USA.
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The exchange lasted more than five minutes - with an interruption from Sen. "We shouldn't have to put up with this kind of stuff". The Capitol Police can't close the room to the public and can't keep out people who look like they might disrupt the hearing.
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He said: "Two matches in a row very tough ones". "They have to go back to Argentina and work again after this tournament. His 56 winners were erased by 59 unforced errors which in turn were three times as many committed by Nadal.
Moore's wife, Kayla Moore, is also listed as a plaintiff in the lawsuit. In the segment, Baron Cohen appeared as the bushy eyebrowed faux counterterrorism instructor "Col. Erran Morad" discussing bogus military technology, including a supposed pedophile detector.
"Morad" then proceeded using the device on Moore as a test, and voila, it immediately began beeping. They are asking for relief in excess of $95 million dollars, not including attorneys' fees.
A Showtime representative wrote in an email that they do not comment on pending litigation, and to their knowledge they had not been served with the complaint.
Mr Moore was not the first public figure duped into a fake interview in a Baron Cohen show.
In the July 29 episode of "Who is America?".
A release form signed by Moore for his appearance on the program, the complaint continues, was invalid due to the supposedly fraudulent conditions under which it was signed.
Baron Cohen has faced past lawsuits over similar pranks, but those actions faltered because the individuals had signed releases.