The problem of optimal data fusion in the sense of the Neyman- Pearson (N-P) test in a centralized fusion center is considered. The fusion center receives data from various distributed sensors. Each sensor implements a N-P test individually and independently of the other sensors. Due to limitations in channel capacity, the sensors transmit their decision instead of raw data. In addition to their decisions, the sensors may transmit one or more bits of quality information. The optimal, in the N-P sense, decision scheme at the fusion center is derived and it is seen that an improvement in the performance of the system beyond that of the most reliable sensor is feasible, even without quality information, for a system of three or more sensors. If quality information bits are also available at the fusion center, the performance of the distributed decision scheme is comparable to that of the centralized N-P test. Several examples are provided and an algorithm for adjusting the threshold level at the fusion center is provided.