When he's had casinos on the line, it's been a different story.
Trump has handed over tax returns in the midst of audits before -- to state gambling officials in Pennsylvania and New Jersey, as part of the process of seeking casino licenses in those states.
The returns haven't been publicly accessible, but they were used by the state investigators who reviewed those applications.
In Pennsylvania, Trump's attorneys included tax returns from 2000 through 2004 in a set of documents that the state's Gaming Control Board stamped as "received" on February 9, 2006.
It came as Trump attempted to build a casino in Philadelphia -- a project that state officials ultimately rejected amid fears he'd use it to lure gamblers across state lines to his properties in Atlantic City, New Jersey, where the tax rate is lower.
He was required to turn over tax returns in New Jersey, as well, where state law requires five years' worth of tax returns from casino license applicants. A spokesman for the New Jersey Casino Control Commission confirmed that Trump's tax returns were mandatory, but said they'd only have been made public if they were introduced as evidence in court proceedings over casino licenses -- which didn't happen in Trump's case.
At least some of the federal and state tax returns he gave Pennsylvania were the subject of ongoing audits at the time. Trump in March released a letter from his attorneys saying that every tax return he's filed since 2002 was audited, and the returns for 2009 and every year since are still the subject of ongoing audits.
Asked why Trump would share returns that were the subject of ongoing audits with state casino licensing officials, but won't release his tax returns now, spokeswoman Hope Hicks would only say in an email Wednesday: "Mr. Trump has always said that when the routine audit is complete he would release his tax returns."
Increasingly, the presumptive Republican nominee is under pressure to release his returns.
Last year, Trump had said he'd release his tax returns. But he has since backed off that pledge, citing ongoing audits and saying he'll offer his returns as soon as those audits are closed.
He told The Associated Press in an interview Tuesday that "there's nothing to learn from them," noting that he has offered a financial disclosure detailing his personal wealth. After the AP reported that Trump would release his tax returns after the election, he took to Twitter to once again point to the end of the audits as the date he'd share them.
Hillary Clinton, the Democratic front-runner, laid into Trump during an event in Camden County, New Jersey, on Wednesday, after a man in the audience raised the issue.
"When you run for president, especially when you become the nominee, that is kind of expected," Clinton said. "My husband and I have released 33 years of tax returns -- we've got eight years on our website right now. So you have got to ask yourself, why does he not release them?"
The pro-Clinton group American Bridge on Wednesday launched a new website, TrumpReleaseYourReturns.com, calling on Trump to do just that.
"Voters deserve to know whether or not Trump pays his fair share in taxes, for example, or if he's too cheap to give to charitable causes," said American Bridge President Jessica Mackler.
Mitt Romney, the 2012 GOP nominee and a fierce Trump critic, reiterated his own call for Trump to release his tax returns in a Facebook post Wednesday afternoon.
"It is disqualifying for a modern-day presidential nominee to refuse to release tax returns to the voters, especially one who has not been subject to public scrutiny in either military or public service," Romney said. "Tax returns provide the public with its sole confirmation of the veracity of a candidate's representations regarding charities, priorities, wealth, tax conformance, and conflicts of interest."
Other presidential candidates have released their tax returns amid audits, too. In 1973, President Richard Nixon publicly released
his returns while they were under audit.