Without the conditional independence assumption, the problem of distributed detection becomes intractable in general. A promising approach for this problem was proposed recently that utilizes a hierarchical conditional independence model. By inserting a hidden variable in the detection hierarchy that induces conditional independence among sensor observations, it is possible to identify certain conditions under which the detection problems become tractable. This paper generalizes the conditions thereby broadening the classes of distributed detection problems with dependent observations that can be readily solved. An example of distributed detection of a random signal is given to show that the proposed generalization can solve problems that were not possible using the original approach.