When all the rules of sensor decision are known, the optimal distributed decision fusion, which relies only on the joint conditional probability densities, can be derived for very general decision systems. They include those systems with interdependent sensor observations and any network structure. It is also valid for m-ary Bayesian decision problems and binary problems under the Neyman-Pearson criterion. Local decision rules of a sensor with communication from other sensors that are optimal for the sensor itself are also presented, which take the form of a generalized likelihood ratio test. Numerical examples are given to reveal some interesting phenomena that communication between sensors can improve performance of a senor decision, but cannot guarantee to improve the global fusion performance when sensor rules were given before fusing. When all the rules of sensor decision are known, the optimal distributed decision fusion, which relies only on the joint conditional probability densities, can be derived for very general decision systems. They include those systems with interdependent sensor observations and any network structure. It is also valid for m-ary Bayesian decision problems and binary problems under the Neyman-Pearson criterion. Local decision rules of a sensor with communication from other sensors that are optimal for the sensor itself are also presented, which take the form of a generalized likelihood ratio test. Numerical examples are given to reveal some interesting phenomena that communication between sensors can improve performance of a senor decision, but can not guarantee to improve the global fusion performance when sensor rules were given before fusing.