“THERE’S A REAL difference between not being criminally charged versus running a campaign properly.” That point, made by U.S. Attorney Ronald C. Machen Jr. this month as he closed the criminal case against Kwame R. Brown’s 2008 reelection campaign, is apparently lost on the former D.C. Council chairman. That’s all the more reason we hope that D.C. election officials are serious about pursuing lingering issues that surround this campaign.

Mr. Machen called upon the D.C. Board of Elections — which had requested the federal investigation — to resume its administrative proceedings into the civil complaint of widespread irregularities and discrepancies in Mr. Brown’s 2008 campaign for reelection to an at-large council seat. The federal investigation resulted in Mr. Brown resigning as chairman and pleading guilty to a misdemeanor charge of violating a city campaign statute and to felony bank fraud unrelated to the campaign. Mr. Brown’s brother, Che Brown, also pleaded guilty to bank fraud.

“The closure of criminal investigation should not be interpreted as a clean bill of health for the 2008 Kwame Brown campaign,” said the statement by Mr. Machen. He noted that “the criminal law is not a panacea for addressing all breaches of the public trust.”

Somehow, though, that distinction, not to mention the significance of his misdeeds, seems to have eluded the disgraced former council member. In a holiday note to supporters obtained by The Post’s Mike DeBonis, Mr. Brown wrote, “It is important to me that you know that I did not violate your public trust.”

This is wrong in at least two ways. First, Mr. Brown incorrectly said that investigators found no crime related to campaign finance abuse. Has he already forgotten standing in Superior Court and becoming the first official in District history to plead guilty to a criminal violation of D.C. campaign laws? Second, he implied that being a cheater is not an abuse of the public trust, as long as the crime isn’t related to official duties. We think that many voters would disagree.

The civil complaint by the Office of Campaign Finance that prompted the federal probe cited serious and numerous violations of regulations on using cash, reporting contributions and setting up accounts. Mr. Brown, as Mr. Machen wrote to the board, expressly confirmed some of these violations through his guilty plea.

The campaign may be defunct, and it may be hard to collect any fines, but the elections board needs to make clear — to Mr. Brown and all other candidates for public office — that it takes seriously its obligation to ensure fair and transparent campaigns.