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Depends on how credible the testimoney of the witness is as well as other circumstantial evidence (like who called 911, what was said, or how law enforcement became involved, what was said to them, etc.). If the prosecutor goes forth with formal charges, they typically do so because they think they can make the case. If they drop the case and don't prosecute, they don't. Contrary to popular belief, having physical evidence is more of the exception than the rule most of the time.
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