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On a 26-day book tour last month, Ben Carson held a news conference in a Books-a-Million store in Iowa, appeared often on TV to discuss his candidacy and sandwiched campaign rallies between book signings.

Now a Democratic watchdog group has complained to the Federal Election Commission that Mr. Carson violated campaign finance law because his publisher paid his travel expenses.

The watchdog group, the American Democracy Legal Fund, charges in its complaint filed Monday that the expenses paid by Mr. Carson’s publisher, Sentinel, a division of Penguin Random House, are in-kind contributions to his campaign. Corporations are banned under federal law from donating directly to a candidate.

Doug Watts, a spokesman for Mr. Carson’s campaign, called the complaint without merit. “Both the campaign and the publisher were meticulous in segregating expenses and activities,’’ he said.

The complaint was signed by Brad Woodhouse, a Democratic operative, who singled out an Oct. 9 appearance at the National Press Club in Washington. It was promoted by Mr. Carson’s publisher, and he answered questions about what he would do as president, including setting up a no-fly zone over Syria.

In a fund-raising appeal this week, a “super PAC” aligned with Mr. Carson boasted that his book tour helped him win supporters.

“Dr. Carson is doing book signings (mostly in early voting states) because it gives him a chance to meet and connect with voters one-on-one,” the chairman of the super PAC, John Philip Sousa IV, wrote to prospective donors. The super PAC, which cannot coordinate with Mr. Carson’s campaign, stationed volunteers at the book signings to collect voter contact information.

“The facts indicate that Dr. Carson has used his Sentinel-funded book tour to openly campaign for federal office,’’ Mr. Woodhouse wrote to the F.E.C.

Many candidates are also authors, and the issue has come before the election commission before. Paul S. Ryan, an expert at the nonpartisan Campaign Legal Center, said candidates were required to pay for any campaign-related events, such as fund-raisers, that they hold on a book tour.

But the issue of travel expenses is a gray area. In 2011, the committee’s six commissioners deadlocked on the question. The three Republican commissioners said it was O.K. for a candidate to hold campaign events on a book tour in which the travel costs were wholly paid by a publisher. The three Democrats on the commission said the candidate should pay a share of travel expenses equal to time spent campaigning.

Given the partisan division, Mr. Ryan said, the committee would most likely deadlock on whether Mr. Carson broke the law if his campaign didn’t pay a fair portion of travel expenses. Because four votes are needed to open an investigation, the Democracy Legal Fund’s challenge is unlikely to go anywhere, campaign law experts said.

“My best guess is, there’s unlikely to be four votes to pursue an investigation,” Mr. Ryan said.

“It takes four to even open up the hood of the car,” said Kenneth A. Gross, who practices political law in Washington.