NEW YORK (AP) — The cover-up is worse than the crime, the expression goes. And in the hush money case against Donald Trump, prosecutors say the cover-up made the crime worse.

In an indictment and other documents unsealed Tuesday, prosecutors say Trump falsified records about three payoffs in order to keep potentially damaging stories from coming to light as he campaigned for the presidency in 2016. Manhattan District Attorney Alvin Bragg said it was Trump's effort to cover up crimes related to that election that allowed prosecutors to charge the 34 counts as felonies.

The indictment, however, raises thorny issues about state and federal law that could provide openings for the defense to try to get the changes tossed before the case even gets to trial.

"The bottom line is that it's murky," said Richard Hasen, an expert in election law and professor at the University of California, Los Angeles law school. "And the district attorney did not offer a detailed legal analysis as to how they can do this, how they can get around these potential hurdles. And it could potentially tie up the case for a long time."

Trump, a candidate for the Republican presidential nomination in 2024, says he did nothing wrong and that the case is a political persecution. In remarks from his Florida home just a few hours after his court appearance, he said, "This fake case was brought only to interfere with the upcoming 2024 election and it should be dropped immediately."

In the end, the case isn't about the tawdry details of the hush money payments, including a central one to porn actor, Stormy Daniels. It's also not about Trump's acrimonious relationship with his onetime lawyer-turned-government witness, Michael Cohen.

It's allegedly about a presidential candidate using his money and influence to bury potentially damaging stories that might make voters choose a political rival, particularly as Trump's reputation was suffering at the time from comments he had made about women.

Falsifying business records can be charged as a misdemeanor, a lower-level crime that would not normally result in prison time. It rises to a felony — which carries up to four years behind bars — if there was an intent to commit or conceal a second crime. Bragg said his office routinely brings felony false business records cases.

In Trump's case, Bragg said the phony business records were designed to cover up alleged state and federal election law violations. The $130,000 payment to Daniels exceeded the federal cap on campaign contributions, Bragg said. He also cited a New York election law that makes it a crime to promote a candidate by unlawful means.

"That is what this defendant did when he falsified business records in order to conceal unlawful efforts to promote his candidacy, and that is why we are here," one of the case prosecutors, Chris Conroy, told the judge Tuesday.

Prosecutors filed a "statement of facts" that told their story of a scheme to protect Trump's presidential prospects by buying and suppressing unflattering information about him. Still, some legal observers were surprised that the indictment itself wasn't more specific about how each of the charges was elevated to a felony.

"There are an awful lot of dots here which it takes a bit of imagination to connect," said Richard Klein, a Touro Law Center criminal law professor. Bragg said the indictment doesn't specify the potential underlying crimes because the law doesn't require it. But given the likelihood of Trump's lawyers challenging it, "you'd think they'd want to be on much firmer ground than some of this stuff," said Klein, a former New York City public defender.

Hasen said it's not clear whether candidates for federal office can be prosecuted in cases involving state election laws. The defense may also argue the case can't be brought in state court if it involves a federal election law.

Prosecutors, however, also alluded to another accusation involving tax law: that Trump's scheme included a plan to mischaracterize the payments to Cohen as income to New York tax authorities.

"They did talk about tax crimes, and I think that could be potentially more compelling for the jury," Renato Mariotti, a former federal prosecutor, said on ABC News. "It's a safer bet than the campaign finance crimes."

Bragg is "going to bring in witnesses, he's going to show a lot of documentary evidence to attempt to demonstrate that all these payments were in furtherance of the presidential campaign," said Jerry H. Goldfeder, a veteran election lawyer in New York and the director of Fordham Law School's Voting Rights and Democracy Project.

"It remains to be seen if he can prove it beyond a reasonable doubt," Goldfeder said. But, he added, "Do not underestimate District Attorney Alvin Bragg and do not overestimate Mr. Trump."

Trump's lawyers have painted him as a victim of extortion who had to make the payments to prevent false and embarrassing information from coming out. They say the payments had nothing to do with the campaign.

It's similar to an argument made by former North Carolina Sen. John Edwards, the Democrat accused of funneling nearly $1 million in under-the-table campaign contributions in an effort to conceal his pregnant lover during his 2008 run for president. Edwards argued the payments were a personal matter, intended to keep the matter secret from his wife. A jury acquitted him on one charge and deadlocked on other counts. He wasn't retried.

The New York case is just one of many legal worries for Trump.

Georgia prosecutors are investigating Trump's attempts by Trump and his allies to overturn his 2020 election loss in in the state. Federal prosecutors are investigating whether classified documents were criminally mishandled at Trump's Florida home, as well as efforts by Trump and his allies to undo the results of the presidential election.

"Bringing a failed prosecution is just going to enable him to claim that it's a witch hunt," Hasen said of Trump. "And it might convince some people that all of the potential criminal cases against Trump are full of spurious claims, whereas I think the other potential cases involving classified documents, the 2020 election, seem much stronger both legally and factually."

Trump's lawyers are certain to attack the credibility of Cohen, a convicted liar who is far from the ideal prosecution witness. The disbarred attorney has said that Trump directed him to arrange the payment of hush money to fend off damage to Trump's White House bid.

Cohen has admitted in court to lying before, and Trump's lawyers will no doubt try to use that to their advantage. Cohen pleaded guilty in 2018 to lying to Congress to cover up that he was negotiating the Moscow Trump Tower project on Trump's behalf during his presidential campaign. Cohen pleaded guilty in a parallel federal case to campaign finance violations and other charges in connection to the hush money payments.

After federal prosecutors declined to file charges against Trump in the hush money case, a former law enforcement official told The Associated Press that prosecutors harbored concerns over the reliability of Cohen as a witness. Federal prosecutors believed it was far from clear that Trump could be convicted of a campaign finance crime, even if a jury believed Cohen's allegations that he directed the hush money payments.

Trump has already indicated he may try to have the case moved out of Manhattan, writing on social media Tuesday that it should be held in Staten Island. He called that borough — which is more conservative than the rest of New York City — "A VERY FAIR AND SECURE LOCATION."

Trump may also argue that the statute of limitations — which is five years for most felonies in New York — has run out because the hush money payments and Cohen's reimbursements happened before then.

There were some extensions during the pandemic, and state law also can stop the clock when a potential defendant is continuously outside the state. Trump visited New York rarely over the four years of his presidency and now lives mostly in Florida and New Jersey. His lawyers could question whether the timeout applies to elected officials serving in Washington.

"This case has some very good issues for the defense to litigate," said Duncan Levin, a New York City defense lawyer and former Manhattan prosecutor. "It's not an open-and-shut case by any means."

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Richer reported from Boston and Long reported from Washington. AP White House Correspondent Zeke Miller contributed to this report.

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EDITOR'S NOTE — Alanna Durkin Richer has written for The Associated Press for more than a decade and covered legal affairs for more than five years; Colleen Long covers the White House for the AP and covered crime and courts in New York for more than a decade; Jennifer Peltz has covered New York for 16 years for the AP, including several years specializing in Manhattan's criminal courts.