Story highlights Howard Dean tweeted during the debate, "Notice Trump sniffing all the time. Coke user?"

His comments have drawn rebuke from within his own Democratic party

(CNN) Howard Dean claimed, with no evidence, that Donald Trump's sniffling at the debate could be due to cocaine use -- a comment that's being ripped as way out of bounds, even by those in his own party.

The former Vermont governor and former chairman of the Democratic National Committee tweeted during Monday night's first presidential debate, "Notice Trump sniffing all the time. Coke user?"

Dean, who has endorsed Hillary Clinton, and the Trump campaign have not responded to a CNN request for comment. The Clinton campaign, for which Dean has acted as a surrogate, also hasn't responded for comment.

Trump has said throughout his life that he doesn't drink alcohol or do drugs, often citing the substance abuse issues his late brother had as a deterrent.

Even some of Dean's allies are swatting down the gossip. David Axelrod, a former top adviser to President Barack Obama and now a CNN contributor, took to Twitter on Wednesday to register his disapproval.

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