Distributed detection with conditionally dependent observations is known to be a challenging problem in decentralized inference. This paper attempts to make progress on this problem by proposing a new framework for distributed detection that builds on a hierarchical conditional independence model. Through the introduction of a hidden variable that induces conditional independence among the sensor observations, the proposed model unifies distributed detection with dependent or independent observations. This new framework allows us to identify several classes of distributed detection problems with dependent observations whose optimal decision rules resemble the ones for the independent case. The new framework induces a decoupling effect on the forms of the optimal local decision rules for these problems, much in the same way as the conditionally independent case. This is in sharp contrast to the general dependent case where the coupling of the forms of local sensor decision rules often renders the problem intractable. Such decoupling enables the use of, for example, the person-by-person optimization approach to find optimal local decision rules. Two classical examples in distributed detection with dependent observations are reexamined under this new framework: detection of a deterministic signal in dependent noises and detection of a random signal in independent noises.