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It sounds like a small-bore infraction: Liz Cheney, a United States Senate candidate in Wyoming, bought a state fishing license last summer even though she had not lived in the state for a year, as required.

But the matter has inflamed her critics in the state, who have already labeled her an interloper and taken issue with her challenge to Senator Michael B. Enzi in next year’s Republican primary. Mr. Enzi is a popular three-term incumbent who is as conservative as Ms. Cheney.

“It’s a serious misstep,” said Liz Brimmer, a Republican strategist in Wyoming and former chief of staff to former Senator Craig Thomas, a Republican. “Allegedly poaching in a state where being a resident sportsman is, by law, an earned privilege. Wyoming people will take this very seriously.”

According to state records, Ms. Cheney, daughter of former Vice President Dick Cheney, bought the $24 game and hunting license in August of 2012 at Westbank Anglers in Teton Village. She had moved to the state the previous May. She is also listed on the application of having lived in Wyoming for 10 years.

Ms. Cheney and her spokeswoman declined requests for an interview. But she told the Star Tribune in Casper, which first reported the story with The Associated Press, “The clerk must have made a mistake. I never claimed to be a 10-year resident.”

She also said she was unaware of the one-year residency requirement.

Alan Dubberley, a spokesman for the Wyoming Game and Fish Department, said the agency was not ready to declare whether Ms. Cheney faced fines. “We have an ongoing investigation,” he said. “The law is extremely complicated.”

In recent interviews in the Jackson Hole area, near where Ms. Cheney lives, many Republicans questioned her candidacy, accusing her of not truly understand Wyoming. She had long lived in Virginia, outside Washington, D.C.

Mark Newcomb, an environmental economist who supports Mr. Enzi, dismissed the Cheney campaign’s contention that she would bring new energy to the state.

“She’s probably as much old guard as anyone else,” he said. “She comes from a political family and she can’t fool me.”

Ms. Cheney, mindful of such criticism, is crisscrossing the sprawling state and keeping her distance from the city she called home until last year. Despite the presence of many friends and former colleagues in the Washington, D.C., area, she has purposefully not held a fund-raiser in the capital in the weeks since she announced her bid.

“She has made multiple visits to all the counties and is now making another round; doing visits and events with Wyoming voters,” said Mary Matalin, a close friend of Ms. Cheney, when asked about the notable absence of Beltway fund-raisers. “To everything there is a season.”

Jonathan Martin contributed reporting.