In this paper, the privacy problem of a parallel distributed detection system vulnerable to an eavesdropper is proposed and studied in the Neyman-Pearson formulation. The privacy leakage is evaluated by a metric related to the Neyman-Pearson criterion. We will show that it is sufficient to consider a deterministic likelihood-ratio test for the optimal detection strategy at the eavesdropped sensor. This fundamental insight helps to simplify the problem to find the optimal privacy-constrained distributed detection system design. The trade-off between the detection performance and privacy leakage is illustrated in a numerical example.