The problem of collaborative distributed hypothesis testing is investigated. In this setting, a binary decision is required about the joint distribution of two arbitrary dependent memoryless processes that are sampled at different physical locations (nodes) in the system. Interactive rate-limited communication is allowed between these nodes. Defining two types of error events, the error exponent for an error of the second type is investigated, under a prescribed probability of error of the first type. A general achievable error exponent, as a function of the total available communication resources, is proposed, for the case of two general hypotheses. The special case of testing against independence is revisited for which it is shown that optimality can be attained, as a special case of the general achievable exponent, provided the constraint over the error probability of the first type goes to zero.