WASHINGTON — Americans hoping that President Donald Trump’s third “annual” physical exam over a span of 13 months on Tuesday might offer insights into his increasingly bizarre and incomprehensible statements and social media posts are likely to be disappointed.

Neither Trump nor his White House is under any legal obligation to reveal observations about his mental health that might be made by the team of physicians who examined him at Walter Reed National Military Medical Center.

Bandy Lee, a psychiatrist and former professor at Yale School of Medicine, said those doctors do, though, have an ethical responsibility to the American people to do just that.

“Of course, the White House physician has a duty, and so do we. The public is being shortchanged, and endangered, to the maximum,” said Lee, who in 2017 edited “The Dangerous Case of Donald Trump,” one of the first warnings from mental health professionals about Trump’s behavior pattern.

“The incoherence is worrisome, possibly dangerous,” said Allen Dyer, a retired psychiatrist and retired George Washington University professor who recommends a full battery of tests. “The evaluation should include a complete mental status exam as well as imaging studies, lab studies, including amyloid studies that might be indicative of Alzheimer’s, which his father was reported to have had, and a battery of cognitive tests.”

Dyer, in 1973, helped craft the so-called “Goldwater rule” that he says has been misinterpreted to mean that mental health professionals should never offer their analyses of political figures.

Last week, Lee and 19 other doctors and mental health professionals wrote to the White House physician, telling him that “Trump’s judgment, decision-making, and relationship to reality are dangerously impaired” and calling on him to take action because Trump is a danger to himself and others.

Trump’s White House said it would provide information in the next day or two about his Walter Reed visit but would not address HuffPost’s queries about his mental health. Trump himself posted on social media Tuesday afternoon: “Everything checked out PERFECTLY.”

Trump has, ever since he entered politics 11 years ago, spoken and written in an over-the-top style. In recent years and especially in recent months, though, his tendency to ramble and answer questions with non-sequiturs appears to have worsened, while his posts on social media have grown ever more unhinged.

He has threatened Iran with civilization-ending genocide and hinted at using nuclear weapons as the war he began on Feb. 28 continues even as Trump tries to declare victory and move on. Early Tuesday, he posted an AI-generated image of him wielding a long gun and standing over a dead rhinoceros, with the statement “NO RINOS!” — a reference to the acronym “Republicans in name only,” which in his view means Republicans who are not sufficiently loyal to him.

While past presidents and presidential candidates have bent over backward to prove they were healthy enough for the job — the late John McCain released more than a thousand pages of medical records when he ran in 2008 — Trump has taken the opposite approach, revealing virtually nothing.

When he first ran in 2016, Trump released no records but did put out a single-page letter under his personal physician’s signature that appeared to have been written by Trump himself. “If elected, Mr. Trump, I can state unequivocally, will be the healthiest individual ever elected to the presidency,” Harold Bornstein wrote.

During his first term, the White House doctor, Ronny Jackson, wound up becoming a big Trump supporter — “If he had a healthier diet over the last 20 years, he might live to be 200,” he told reporters in 2018 — and eventually ran for and won a House seat from Texas with Trump’s backing.

During this current term, the White House has deflected questions about his health and given at times nonsensical answers. The deep bruising on his right hand, for example, was explained away as resulting from shaking so many hands, even though it was on the back of his hand, which is not touched during a handshake. Eventually the bruises showed up on his left hand, as well.

While Trump’s White House doctors and aides almost certainly will not reveal any information about whether his mental condition was examined, it is possible that Trump may himself do so, the same way he let the world know that his doctors had administered to him a screening test for dementia.

The simple, 30-question Montreal Cognitive Assessment is designed to provide doctors early warning signs of loss of mental acuity. Trump, instead, has repeatedly claimed over the several years since it was first administered to him that it proves his genius.

“I’ve taken it and I’ve aced it all three times, I’ll tell you, because it is a positive thing,” he boasted again Friday at a political rally.

Dyer said Trump’s claims about the MoCA test are further evidence of his issues. “His bragging about ‘acing’ the Montreal screening test, being able to distinguish two animals, is suggestive for poor judgment rather than cognitive sharpness,” he said,

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