Performing likelihood ratio based detection with high dimensional multimodal data is a challenging problem since the computation of the joint probability density functions (pdfs) in the presence of inter-modal dependence is difficult. While some computationally expensive approaches have been proposed for dependent multimodal data fusion (e.g., based on copula theory), a commonly used tractable approach is to compute the joint pdf as the product of marginal pdfs ignoring dependence. However, this method leads to poor performance when the data is strongly dependent. In this paper, we consider the problem of detection when dependence among multimodal data is modeled in a compressed domain where compression is obtained using low dimensional random projections. We employ a Gaussian approximation while modeling inter-modal dependence in the compressed domain which is computationally more efficient. We show that, under certain conditions, detection with multimodal dependent data in the compressed domain with a small number of compressed measurements yields enhanced performance compared to detection with high dimensional data via either the product approach or other suboptimal fusion approaches proposed in the literature.