This paper considers a decentralized detection system for a binary hypothesis testing problem. The sensor signals are marginally Gaussian distributed with θ-parameter Clayton copula joint distribution. Boolean functions of two variables and likelihood ratio test at the fusion center are considered to generate binary global decisions. The exhaustive search and the genetic algorithms are proposed to provide the local sensor decision rules in each scenario such that the probability of error at the fusion center is minimized. The main purpose of this paper is to study the probability of error behavior of the proposed detection systems in a correlated environment characterized by a joint Clayton copula distribution. The results show that in a correlated environment a sound detection system should be characterized by the likelihood ratio test at the fusion center and multiple-threshold decisions at the sensors.