Judge James Otero said Michael Cohen’s constitutional rights could be endangered if the case proceeded while he was under criminal investigation.
The actress is seeking to end a non-disclosure deal signed over an alleged relation with Donald Trump in 2006.
Michael Cohen had said he would invoke his right to remain silent over the case.
The lawyer had argued that any statement he made in court could affect a criminal inquiry in New York into his business affairs.
As part of the investigation into the Daniels case, the FBI raided Michael Cohen’s offices for information, including on the non-disclosure agreement with Stormy Daniels – whose real name is Stephanie Clifford – signed days before the 2016 presidential election.
District Judge Otero in Los Angeles said there was “a large potential factual overlap” between the civil and criminal proceedings against Michael Cohen.
The judge said that “would heavily implicate Mr. Cohen’s Fifth Amendment rights”, in a reference to the Constitution’s protection against self-incrimination.
Michael Cohen’s lawyers had earlier asked for the Daniels case to be put on hold for three months.
They had argued that Michael Cohen faced a Catch-22 situation: giving evidence in Los Angeles might mean incriminating himself in New York; while invoking his right to silence in the civil suit could undermine his defense there.
Catch-22 states that no individual can be “compelled in any criminal case to be a witness against himself”.
Invoking the amendment means Michael Cohen will not have to reveal sensitive information in the wider investigation into his affairs.
A lawyer for Stormy Daniels, Michael Avenatti, earlier described Michael Cohen’s move as a “stunning development”.
The raid on Michael Cohen followed a tip-off by the office of Special Counsel Robert Mueller, who is investigating alleged Russian interference in the 2016 presidential election and possible collusion with the Trump campaign.
Russia denies interfering in the election and President Trump has denied any collusion.
Separately, Stormy Daniels alleges she had a relationship with Donald Trump in 2006.
President Trump has denied having any relation with Stormy Daniels or any knowledge of the $130,000 payment to her by Michael Cohen during the 2016 presidential campaign.
Stormy Daniels says she accepted the sum in return for signing the non-disclosure agreement.
During a recent TV interview, Stormy Daniels said she had been threatened in 2011 in a Las Vegas car park while she was with her infant daughter, and had been told to keep quiet about her alleged relationship with Donald Trump.
Stormy Daniels is now suing President Trump in an attempt to invalidate the non-disclosure agreement, which she alleges is invalid because he did not sign it personally.
Legal analysts have said that Michael Cohen’s $130,000 payment to Stormy Daniels could have violated the rules on financing Donald Trump’s 2016 presidential campaign.
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