The problem of decision fusion in distributed sensor system is considered. Distributed sensors pass their decisions about the same hypotheses to a fusion center that combines them into a final decision. Assuming that the semor decisions are independent from each other conditioned on each hypothesis, we provide a general proof that the optimal decision scheme that maximizes the probability of detection at the fusion for fixed false alarm probability comists of a Neyman-Pearson test (or a randomized N-P test) at the fusion and likelihood-ratio tests at the sensors