Hours after he was fingerprinted, booked and entered a "not guilty" plea in federal court in Miami, former President Donald Trump defied the very premise of the federal government's case against him, claiming presidents have an "absolute right" to keep any and all documents they want. 

Trump pleaded not guilty in federal court to more than three dozen criminal counts, including willful retention of classified records and obstruction of justice. Trump was released on his own recognizance Tuesday afternoon, and did not have to give up his passport or submit to other restrictions — except the restriction that he cannot discuss the case with possible witnesses. He was also ordered not to discuss the case with his co-defendant, Walt Nauta, a Trump aide who is charged with six counts in the case and also appeared in court Tuesday.    

But on Tuesday night, surrounded by buoyant supporters at his own club in Bedminster, New Jersey, Trump claimed he had "every right to have these documents" under the Presidential Records Act. Trump suggested outgoing presidents can take any records they like with them. 

• What does the Presidential Records Act say, and how does it apply to Trump?

"Whatever documents a president decides to take with him, he has the right to do so. It's an absolute right. This is the law," Trump said. 

Except, that isn't an absolute right, according to not just the prosecution, but legal experts and the wording of the Presidential Records Act itself. 

The Presidential Records Act lays out the difference between "personal" records — things like family photos — and presidential records. 

"The Presidential Records Act distinguishes between documentary materials created or received by a president and his immediate staff in the course of conducting the official duties of the president, and 'personal records' that a president can take with him at the end of his time in the White House," Jason R. Baron, former director of litigation at the National Archives and Records Administration, told CBS News. "As defined under the statute, personal records consist of materials such as diaries, journals or personal notes which are not prepared for, utilized for, or circulated or communicated in the course of transacting government business. That definition is very narrow. There is absolutely no legal authority that supports the idea that a president could assert, for example, that classified records are 'personal.' That would still be true even if such records were declassified."

Under the Presidential Records Act, presidents are to turn over all records by the time they are no longer president, meaning, by noon on Jan. 20.

"Upon the conclusion of a President's term of office, or if a President serves consecutive terms upon the conclusion of the last term, the Archivist of the United States shall assume responsibility for the custody, control, and preservation of, and access to, the Presidential records of that President," the PRA reads. 

Baron said the former president "simply is wrong in saying that he had an absolute right to take official documents with him when he left office."

"Under the Presidential Records Act, legal custody of presidential records immediately passes to the Archivist of the United States when a new president is sworn in," Baron continued. "That means as of January 20, 2021, former President Trump had no right to retain any official record about White House business. Not a single one. And once he was notified by staff at the National Archives, he had a legal duty to return every presidential record he retained at Mar-A-Lago, whether those records were classified or not."   

The case against Trump focuses on his handling of classified records, not just any presidential records. The indictment says that after his presidency, "Trump was not authorized to possess or retain classified documents," and yet, Trump "caused scores of boxes, many of which contained classified documents, to be transported to The Mar-a-Lago Club in Palm Beach, Florida." 

As he made the case for his defense Tuesday night, Trump referenced a 13-year-old case in which the right-leaning group Judicial Watch demanded 79 tape recordings of former President Bill Clinton when he was in office. Clinton had designated the records as personal, and Judicial Watch ultimately lost the case, with the presiding judge saying she could not order the National Archives to reclassify them and "this responsibility is left solely to the president." It's a case that's likely to come up in Trump's defense. 

Trump also claimed Tuesday night that "the president enjoys unconstrained authority to make decisions regarding the disposal of documents."

But the PRA doesn't permit presidents while in office to dispose of a presidential record without a process. 

The Presidential Records Act says: "During the President's term of office, the President may dispose of those Presidential records of such President that no longer have administrative, historical, informational, or evidentiary value if--(1) the President obtains the views, in writing, of the Archivist concerning the proposed disposal of such Presidential records; and (2) the Archivist states that the Archivist does not intend to take any action under subsection (e) of this section."

On Tuesday night, Trump began his remarks by calling his indictment and arraignment, "the most evil and heinous abuse of power in the history of our country." 

"A corrupt sitting president had his top political opponent arrested on fake and fabricated charges of which he and numerous other presidents would be guilty, right in the middle of a presidential election in which he is losing very badly," Trump said of President Biden. 

"This day will go down in infamy and Joe Biden will forever be remembered as not only the most corrupt president in the history of our country but perhaps even more importantly, the president who together with the band of his closest thugs, misfits and marxists tried to destroy American democracy," added Trump, whom special counsel Jack Smith is also investigating for his alleged role in the effort to overturn the 2020 presidential election on Jan. 6, 2021. 

Before concluding his speech, Trump said — if he were to win the 2024 presidential election — he would do the thing he accuses Mr. Biden of doing — appointing a prosecutor to go after a political opponent.

"I will appoint a real special prosecutor to go after the most corrupt president in the history of the United States of America, Joe Biden, and the entire Biden crime family," Trump said. 

Trump raised more than $2 million at the Bedminster fundraising event following his speech, according two two sources, including one donor at the event. 

— Fin Gomez contributed reporting to this story 

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Kathryn Watson is a politics reporter for CBS News Digital based in Washington, D.C.