In the suit, Underwood also accuses Trump of turning his charity into a tool of his 2016 presidential campaign, despite prohibitions on political activity by nonprofit entities. She also laid out her findings in a letter to the IRS, suggesting that federal authorities investigate further.
It is a felony to knowingly file a false tax return, with potential penalties of up to US$100,000 ($144,780) in fines and up to three years in prison. In rare cases - where prosecutors could prove the falsehood to be deliberate - people have been convicted of signing false tax returns.
The IRS declined to comment.
If the government does try to prosecute Trump - a very big "if," given the difficulty of such cases and the debate about whether sitting presidents can be prosecuted - Trump would face questions about whether he knowingly broke charity laws.
If federal officials do not pursue a criminal case against Trump, legal experts said, the tax agency could face its own quandary. Why should other taxpayers be punished for violating the same rules that the president has now been accused of breaking?
"The IRS depends on citizens not lying on their tax returns," said Marc Owens, the former head of the IRS's nonprofits division. If the IRS does not take visible action on Trump's false statements, he said, "it kind of calls into question, 'If they don't prosecute him, does everybody get a pass?' "
The White House, the Trump Organisation, Trump's tax lawyers and Trump's longtime accountant did not respond to requests for comment.
Last week, Trump described the lawsuit as a political attack by New York Democrats, although the current New York attorney general, Underwood, is a nonpolitician who was appointed to her post. "I won't settle this case!" Trump wrote on Twitter.
In filings to the IRS, Trump's foundation offered a separate defense: Clerical errors caused the foundation to make payments it should not have, and Trump knew so little about charity rules that he broke the law without knowing it.
"Neither the Foundation nor [Trump] knew," the group wrote in an IRS filing, it was wrong to use foundation money to buy a portrait that hung on a wall in one of Trump's golf resorts.
The annual tax returns Trump signed, called the IRS Form 990, are intended to give regulators and donors a look inside a charity's books. They list the donations and expenditures and include several dozen questions that ask whether the charity broke any tax laws in the past year.
Through the 2000s and this decade, Trump repeatedly asserted on state and federal forms that his foundation was following the law.
Underwood's complaint alleges otherwise.
In 2007, for instance, Trump used US$100,000 from his foundation to settle a legal dispute between his Mar-a-Lago Club and the town of Palm Beach, Florida, The Post previously reported. As part of the settlement, the for-profit beach club had pledged to make a donation to a veterans charity.
But the Trump Foundation made the gift instead, according to the town of Palm Beach. Trump's club gave nothing.
When the charity filed its tax return for the year, it did not disclose the nature of this payment, records show.
One of the questions on the 990 asks whether a charity has transferred "any income or assets to a disqualified person." The term "disqualified person" refers to a category of person including an officer of a charity.
Trump was an officer: He was the charity's president. So, the New York attorney general said, the charity had just transferred money in a way that saved Trump's business US$100,000. Because Trump controls the business, Underwood said, this amounted to transferring assets to a "disqualified person."
But on that question, the Trump Foundation checked the box marked "no."
Trump signed the return.
The same thing happened in 2012, when Trump used foundation assets - this time, US$158,000 - to settle a legal dispute with a man who had sued one of his New York golf clubs over a negated hole-in-one prize.
The golf club agreed to make a donation. The charity made the gift instead, according to the lawsuit.
Then, in 2013, the Trump Foundation paid US$5,000 to put an ad for Trump's hotel chain in the program for a charity gala. And in 2014, Trump used US$10,000 of the charity's money to buy a portrait of himself, which his employees hung on a wall in a sports bar at a Trump golf resort in Florida. Both instances were first reported by The Post and confirmed by the attorney general's investigation.
Each year, the form asked the same question about whether the charity had transferred assets for the benefit of a disqualified person.
Each year, the "no" box was checked.
In 2013, Trump gave US$25,000 of the charity's money to a political committee supporting Florida Attorney General Pam Bondi, R. By law, charities are not allowed to make political gifts.
On that year's return, as always, the IRS asked whether the Trump Foundation had spent more than US$100 for "political purposes."
The box checked was "no."
Also, the Trump Foundation omitted any mention of the gift to Bondi's group when the form asked it to list all outgoing donations. Instead, Trump's charity listed a different gift in its place: It told the IRS it had given US$25,000 to a separate group, in Kansas, with a name similar to Bondi's political group. But the Kansas group told The Post it never received a donation.
At the end of that form was rgw same signature box and the same warning about providing false information.
"Under penalties of perjury, I declare that I have examined this return . . . and to the best of my knowledge and belief, it is true, correct and complete."
Trump signed it.
If the IRS decided to investigate the Trump foundation, one key question would be whether Trump knew the forms were incorrect, tax experts said.
"There's the adage, 'Ignorance is no excuse.' That's not true in tax law. In tax law, ignorance is an excuse for criminal violations," said Guinevere Moore, a Chicago attorney specializing in tax cases.
The idea, Moore said, is that tax law is so complicated that prosecutors cannot presume people know they are breaking it.
Federal prosecutors have charged people with filing false charity returns. But in many those cases, they had slam-dunk evidence indicating the defendants understood their returns were false, such as defendants who omitted personal payments or conspired via email to omit embarrassing information from the public filings, experts said.
The president's strategy, so far, has been to plead ignorance. In filings with the IRS - detailed in the New York attorney general's suit - Trump blamed the gift to Bondi on a clerical error and said another clerical error had resulted in a nonexistent gift being listed in its place.
"Mr. Trump learned of the mistake from the news media," much later, the foundation wrote to the IRS.
After The Post's reporting and the launch of the New York attorney general's investigation, Trump repaid his foundation for its expenditures. His golf club took down the portrait. He also assessed himself US$4,000 in penalty taxes in total on three of the transactions - the portrait, the gala program and the donation to Bondi.
But some tax-law experts said that in the unlikely event Trump winds up in a criminal court, it may be hard to convince a jury that a man of his business experience was so unsophisticated, for so long, about his own charity.
"You could try. But I think it's probably a loser," said Christopher Rizek, an attorney at Caplin & Drysdale who has defended clients in tax cases. "You've got a guy who's bragged for years about how smart he is, and how much tax law he knows. And now all of a sudden he doesn't know anything?"
If, on the other hand, the IRS does not pursue any public punishment against Trump - but, rather, does nothing or pursues civil penalties in secret - lawyers said they worry the effect would be to erode other taxpayers' willingness to follow the law.
"Our system of taxation relies on people believing that it's fair and just and - above all - equally applied, no matter if you're rich or poor," said Moore, the Chicago attorney. "It would have an extremely detrimental effect" if Trump faced no obvious punishment for flouting the system.
Already, Moore said, she sees signs that taxpayers have been influenced by Trump's approach toward his charity, as well as the way he bragged during the 2016 campaign that trying to avoid taxes "makes me smart."
When she meets with new clients facing demands from the IRS, Moore said, they often say of Trump: "He doesn't pay his fair share and gets away with it. Why are they coming after me for this?"