The sheriff's office said the two people involved knew each other and had some type of argument that led to them firing shots at each other.
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One person was pronounced dead at the scene.
The other person left and drove to Battleboro, where he stopped at a convenience store and realized he had also been shot.
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He was taken to a hospital and his condition was not immediately available.
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The sheriff's office has not yet released the names of the people involved.
The case remains under investigation and deputies are interviewing witnesses.