Paul Alan Levy of Public Citizen — who is representing the candidate — has the details; I’ve looked into the case, and I agree with his analysis:

The city of Mesa, Arizona, has threatened suit against a local businessman, Jeremy Whittaker, who is running for city council in opposition to a longtime city employee who enjoys endorsements from several current elected city officials. His offense? His lawn signs and campaign literature include a single-color version of the city’s logo … as a handy way of identifying the office for which he is running. City officials told him he can’t use the city logo on his campaign materials because the city has trademark rights in the logo and, supposedly, a trademark can never be used without its owner’s permission. Last week they upped the ante: the city’s outside IP counsel sent him a stiff cease-and-desist letter claiming that Whittaker has infringed the city’s logo and demanding that he turn over all of his campaign material (presumably for destruction).
There are several reason why this demand is wrong — Whittaker is making a purely noncommercial use of the logo which is therefore outside the scope of the Lanham Act and, indeed, protected by the First Amendment, and, in any event, nothing about his material suggests that the city is behind his campaign. Beyond that, the logo is used to identify the city as the subject of his campaign for office, which is fair use.
And then there is this lurking problem: section 2(b) of the Lanham Act forbids the registration of any “flag or coat of arms or other insignia of … any State or municipality” as a trademark. The Trademark Office has apparently been using a narrow construction of this statutory limitation to allow agencies to register logos to identify specific government services or programs. A couple of years ago, a federal judge in New Jersey expressed grave reservations about the very idea of a government trademark in its own seal…. By identifying the symbol at issue as the city’s official insignia, its lawyer might have unwittingly put his client’s trademark registration at risk.
In a letter today to the city’s counsel, I have explained that Whittaker is not going to give in to the incumbents’ trademark bullying. I expect that this will be the end of the matter. If not, my thanks to Al Schmeiser for his willingness to be local counsel.

Visit Paul’s post for pointers to the relevant documents, including the city’s letter and his letter.