In this paper, optimum design of distributed detection is considered for a parallel sensor network system consisting of a fusion center and two passive sonar nodes. AND rule and OR rule are employed as the fusion rules of the sensor network. For the fusion rules, it is shown that a threshold rule of each sensor node has uniformly most powerful properties. Optimum threshold for each sensor is investigated that maximizes the probability of detection under the constraint of a specified probability of false alarm. It is also investigated through numerical experiments how signal strength, false alarm probability, and the distance between two sensor nodes affect the system detection performances.