The Manhattan district attorney on Tuesday released a 34-count unsealed indictment against former President Donald Trump for his alleged role in efforts to bury damaging stories about his personal life ahead of the 2016 presidential election, accusing him of taking part in a years-long "catch and kill scheme" to propel his rise to the White House.

The indictment, the first to accuse a sitting or former U.S. president of a crime, and an accompanying statement of facts accused Trump of unlawfully falsifying business records to cover up hush money payments to individuals who claimed to have negative stories about him, including adult film star Stormy Daniels, who claimed she had an extramarital affair with the former president. Trump has denied having an affair with Daniels or another woman who was paid in exchange for her silence. 

Trump on Tuesday pleaded not guilty to the charges inside Manhattan Criminal Court after being booked and fingerprinted. Trump was quickly released, as is standard for defendants accused of nonviolent crimes.

While the indictment against a former president is an extraordinary development in U.S. history, legal experts noted Trump's conviction is far from assured, saying it will not be easy for Manhattan prosecutors to prove the former president committed a felony.

The falsification of business records is typically a misdemeanor offense under New York state law. But it can be upgraded to a low-level felony if the prosecution can show the defendant committed the offense with the intention to commit or conceal another crime. The 34 counts unveiled by Manhattan District Attorney Alvin Bragg on Tuesday were all felony charges, with prosecutors arguing the former president also violated election laws.

Randy Zelin, a Cornell Law School professor who previously worked as a white collar defense lawyer and prosecutor, said Bragg could face significant hurdles in convincing a jury that Trump intended to commit or conceal another crime when he allegedly falsified business records to conceal the hush money payments.

"I think it will be difficult to prevail on the felonies," Zelin told CBS News. "The falsifying of entries misdemeanor — that's a slam dunk."

Jessica Levinson, a CBS News legal analyst and Loyola Law School professor, said it appears Manhattan prosecutors have a "very strong case" to argue that false business entries were made as part of the "catch and kill" strategy to suppress negative stories about Trump. But she agreed that connecting that alleged offense with violations of election laws or other crimes will be more challenging. 

"Unless you have a smoking gun, showing intent to commit another crime can always be a challenge," she said.

Still, Levinson said Bragg's case does not only hinge on the accounts of former Trump "fixer" Michael Cohen, who she said could be characterized as an unreliable source. Cohen, who said he made a $130,000 hush money payment to Daniels in 2016 on behalf of the former president, served time in federal prison after pleading guilty to tax evasion and campaign finance violations.

"It hinges on David Pecker," Levinson said, referring to the former CEO of America Media, Inc., who allegedly worked with Cohen and Trump to buy and kill negative stories about Trump. "And I think it hinges on other people in the Trump Organization who actually helped him make these payments." 

John Coffee, a Columbia University professor who studies white collar crime, said Trump's lawyers will likely seek to dismiss the case and to change the venue of the proceedings to another jurisdiction. Trump's attorneys, Coffee said, could argue that the case should be dismissed because prosecutors have not sufficiently demonstrated that the former president falsified records to conceal another crime.

"I think they have strong evidence that there were false documents filed for the misdemeanor but I don't understand what they're alleging was the federal offense or the state offense that was covered up," Coffee told CBS News.

Zelin, the Cornell University professor, said the main argument of Trump's legal team could be that the hush money payments were made to protect his family, not to influence the outcome of the 2016 election.

Trump could argue, "I was just trying to be a good husband and a good father. I was trying to keep this out of the press," Zelin said.

But Levinson said that argument could be undermined by evidence that Trump, Cohen, Pecker and others met to bury negative stories about the former president to insulate his presidential candidacy from political attacks and scandals.

"All the allegations point to the idea that some people sat down and said, 'Let's make sure we suppress these stories because we don't want it to get out to the voters,'" Levinson added.