A Washington watchdog group is calling on the Federal Election Commission to investigate irregular payments from a Wisconsin advocacy group to Herman Cain’s presidential campaign.

Citizens for Responsibility and Ethics in Washington, or CREW, alleges in an FEC complaint filed Friday that Cain’s campaign committee violated federal law by failing to report about $40,000 in debts to Prosperity USA, a nonprofit charity founded by Cain chief of staff Mark J. Block.

In addition, the complaint says, Prosperity USA violated laws prohibiting a charity from contributing to a political campaign by paying for airline flights, lodging and other costs in the early weeks of Cain’s exploratory presidential bid.

The complaint argues that Block was central to both sets of alleged violations. “This makes Mr. Block the first person in the history of the [Federal Election Campaign] Act to have both given and received the same illegal contributions,” CREW said in a news release.

The financial questions come amid a separate furor over sexual harrassment complaints lodged against Cain when he was head of a restaurant trade group in the 1990s. That scandal has not dented his standing among GOP primary voters, however, with the latest Washington Post-ABC News poll showing him even with former Massachusetts governor Mitt Romney.

The Milwaukee Journal Sentinel reported earlier this week that Prosperity USA covered Cain’s costs for a $15,000 trip to Atlanta, $17,000 in chartered plane flights, and $5,000 in travel and meeting costs in Iowa, Las Vegas, Houston, Dallas and Louisiana. The newspaper also said the Cain campaign was billed $3,700 for iPads.

Block said earlier this week that the campaign would retain an outside counsel to examine the reports, but declined to identify who was hired. Cain said in a television interview that he was not aware of the alleged payments by Prosperity USA.

An FEC complaint provides no guarantee that the often sluggish agency will actually investigate the case. But Melanie Sloan, the watchdog group’s executive director, said it is “not sufficient for the Cain campaign to investigate itself.”

“As hard as Mr. Cain is trying to prove himself a different kind of candidate, he still has to play by the same rules as everyone else,” Sloan said in a statement. “...Rather, the FEC --the federal agency charged with enforcing campaign finance laws--must look into the matter.”