Distributed detection with conditionally independent observations at local sensors is well understood. The problem becomes significantly more complicated when dependence is present among sensor observations. In this paper, we attempt to make progress in our understanding of the dependent observation case. Toward this end, we present a new hierarchical model by introducing a hidden or latent variable; this model attempts to present a unified framework for distributed detection with conditionally dependent or independent observations. By a close examination of this model, we identify a class of distributed detection problems with conditionally dependent observations whose optimal sensor signaling structure resem bles that of the independent case. This class of problems exhibits a decoupling effect on the form of the optimal local decision rules, much in the same way as the conditionally independent case. Important cases of this class of problems include both the previously known Gaussian case under certain parameter regimes as well as several problems first introduced in this paper. An example is given to illustrate the proposed design approach.