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Mr. Blumenthal repeatedly has apologized, saying he misspoke and did not try to mislead anyone into thinking he served in Vietnam.

Former state Republican Party chairman Robert Poliner said Mr. Simmons is the better candidate for the GOP, especially given his military record. He also said Mrs. McMahon’s association with the wrestling business is “not going to be an easy sell to the general population” because of its violent images and the way it portrays women.

“Then comes along Rob Simmons who doesn’t have these skeletons sitting in his closet and who has a distinguished record of service, of public service,” said Mr. Poliner, who lives in Mr. Simmons‘ old congressional district.

But Patricia Longo, one of the state’s two representatives to the Republican National Committee, said she doubts Mr. Simmons can defeat Mrs. McMahon. While he’s popular on the eastern side of the state, Mrs. McMahon enjoys strong support from Republican-rich southwestern Connecticut, where she lives and where WWE’s headquarters is located, she said.

Those voters don’t seem to be bothered by any controversy surrounding the wrestling empire. They look at Mrs. McMahon as a successful businesswoman, Miss Longo said.

“Do you know how many wrestling fans we have in Connecticut? It’s a legitimate entertainment source and people watch it,” Miss Longo said. “Look at what she’s accomplished. It’s astounding.”