We are a little worried about Rudy Giuliani, the Republican former mayor of New York. Is “America’s mayor” OK?

During his 15-minute speech at the GOP convention last month in Cleveland, it was notable that when he said Donald Trump loves “all people, from the top to the bottom,” Giuliani animatedly gestured toward his knees as he said “top” and above his head as he said “bottom.” Also, why did he say that he and his wife, Judith, have been friends with Trump for 30 years, though he met his wife in 1999, only 17 years ago?

Also — we’re noting this purely out of concern — during his speech he often licked his lips, indicating dry mouth, which, according to the Mayo Clinic, can be a symptom of nerve damage, stroke or Alzheimer’s disease. At the end of his address, beads of sweat were visible on his pâté — did that not suggest heart disease?

Giuliani is just 72, but he seemed slightly stooped as he walked to the lectern, where his wide stance made us wonder if he’s unsteady on his feet. Then there was his slurred diction, as when he referred to “justified” police shootings and Syrian “refyoongees.” More evidence of a stroke?

Yes, all of the above is ludicrous — as ludicrous as Giuliani’s own loathsome smears and innuendo about Hillary Clinton’s health, which follow Trump’s. In recent days, indulging a grudge he has evidently held for years, he has urged people to watch internet videos that purport to prove Clinton is ill.

Of course, Giuliani hasn’t a speck of evidence for his blather, a damning fact considering he was once a federal prosecutor, and proof positive of his impaired character, if not health.

Unfortunately, Trump, 70, has taken the same nondisclosure stance on his health records as he has on his taxes, asserting there is nothing to hide while hiding everything. Clinton, by contrast, has released some test results, which, as far as they go, indicate good health.

That hasn’t stopped Giuliani from trading in scurrilous and debunked theories about the Democratic candidate. Come to think of it, he should see a doctor.