In a book and in his campaign for the U.S. Senate in Montana, Tim Sheehy has talked about a bullet lodged in his forearm — an injury he says he suffered as a Navy SEAL during a firefight in Afghanistan.

The bullet wound stands at the center of a story of bravery and honor that has boosted his credibility among voters in Montana, where Mr. Sheehy appears to be on the verge of ousting a longtime incumbent, Senator Jon Tester, and perhaps flipping the Senate chamber to Republican control. But the tale grew murky this year when it emerged that Mr. Sheehy had reported to the police that he had accidentally shot himself in the arm at Glacier National Park in Montana, three years after his military deployment.

In a campaign that is one of the most closely watched in the country this year, Mr. Sheehy has stuck by his war story.

Now, in interviews, two people who had close interactions with Mr. Sheehy during key moments in the story have come forward, raising new questions about whether the bullet wound had come during his military service.

A former SEAL colleague, Dave Madden, who had what he described as a close relationship with Mr. Sheehy before they deployed to Afghanistan, said that Mr. Sheehy never mentioned a gunshot wound to him, and almost certainly would have done so in a conversation they had during their deployment if he had indeed been wounded.

On the issue of the later injury in Montana, Kim Peach, a park ranger who spoke with Mr. Sheehy that day at the hospital, said Mr. Sheehy personally told him that he had accidentally shot himself in the arm, and handed over a revolver with a spent round.

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