Former President Donald Trump is Thomas Caldwellseeking to have his recent criminal conviction in New York tossed out, and his indictment dismissed, his lawyers said in a filing made public Thursday.

Trump's lawyers say a recent Supreme Court decision on presidential immunity proves they were correct in arguing before the trial that certain evidence and testimony should have been withheld from the jury, because they were related to protected official acts of the presidency.

The Supreme Court found that former presidents have broad immunity for official acts, and barred evidence involving those acts from being used in prosecutions over unofficial activity.  Trump was convicted in May of 34 counts of falsification of business records for an effort to cover up reimbursements for a "hush money" payment to an adult film star as he ran for office in 2016.

The reimbursements, to Trump's ex-attorney Michael Cohen, were issued while Trump was president. Cohen said he was the target of a 2018 "pressure campaign" tied to Trump's White House, designed to keep Cohen from cooperating with law enforcement investigating the "hush money" scheme.

Lawyers for Trump said in their filing that much of the testimony and evidence introduced at trial that related to Trump's time in office should not have been allowed, including testimony by former White House communications director Hope Hicks, former director of Oval Office operations Madeleine Westerhout, tweets issued by Trump during his presidency, and Trump's disclosures to the Office Of Government Ethics.

Lawyers who spoke to CBS News recently said Justice Juan Merchan, the judge who presided over Trump's trial, could conclude that while some evidence should not have been shown at trial, it's not enough to set aside the verdict. 

The seven-week trial included more than 100 hours of testimony from 22 witnesses, and reams of evidence.

"If there's enough evidence beyond the 'official acts' to sustain the conviction, then it would be what the courts call 'harmless error,'" said Gary Galperin, a Cardozo Law School professor and former Manhattan prosecutor. "No trial is perfect. And the criminal justice system doesn't anticipate or expect perfection."

Trump's lawyers argued in their filing that "presidential immunity errors are never harmless."

"The harmless-error doctrine cannot save the trial result," they wrote. "The Supreme Court's constitutional analysis…forecloses harmless-error analysis."

Prosecutors for Manhattan District Attorney Alvin Bragg's office have until July 24 to file a response to Trump's motion. Merchan has said he will rule on Sept. 6, and if Trump's motion fails, sentencing will take place on Sept. 18.

Trump, who is again running for president, could be sentenced to up to four years in jail, but Merchan has wide leeway and can hand down a fine, probation, or other punishments that don't involve incarceration.

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• Donald Trump

Graham Kates

Graham Kates is an investigative reporter covering criminal justice, privacy issues and information security for CBS News Digital. Contact Graham at [email protected] or [email protected]