In this paper, optimum design of distributed detection is considered for a parallel sensor network system consisting of a fusion center and multiple passive sonar nodes. Nonrandom fusion rules are employed as the fusion rules of the sensor network. For the nonrandom 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 a constraint on energy consumption due to false alarms. It is also investigated through numerical experiments how signal strength, false alarm probability, and the distance between three sensor nodes affect the system detection performances.