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The police officer who brought down a gunman after he went on a shooting rampage at the Fort Hood Army base here was on the way to have her car repaired when she responded to a police radio report of gunfire at a center where soldiers are processed before being sent overseas, the authorities said Friday.

As she pulled up to the center, the officer, Sgt. Kimberly Denise Munley, spotted the gunman, later identified as Maj. Nidal Malik Hasan, brandishing a pistol and chasing a wounded soldier outside the building, said Chuck Medley, the director of emergency services at the base.

Sergeant Munley — a woman with a fierce love of hunting, surfing and other outdoor sports — bolted from her car, yanked her pistol out and shot at Major Hasan. He turned on her and began to fire. She ran toward him, continuing to fire, and both she and Major Hasan went down with several bullet wounds, Mr. Medley said.

Whether Sergeant Munley was solely responsible for taking down Major Hasan or whether he was also hit by gunfire from her partner is unclear, but she was the first to fire at him, the authorities said.