The recent findings of high heterogeneity of human breast tissue and much lower than predicted dielectric contrast between tumors and their host tissue have raised questions about the potential utility of stand-alone microwave breast imaging techniques. Multimodal approaches that employ microwaves together with other imaging techniques seem more promising. This study investigates a CT-microwave combination in which microwave detection makes use of prior information obtained from volumetric CT scans and knowledge of tissue dielectric properties. In particular, a detailed patient-specific tissue distribution is first obtained from a 3D-CT scan of the breast under exam. It is assumed that from this scan a limited suspect region is identified. Then from recent research results on the dielectric properties of breast tissue, complex permittivity (dielectric constant and conductivity) maps of the breast can be constructed under the hypotheses of normal and cancerous tissue in the suspect region. These in turn can be used with electromagnetic (EM) simulation software to generate empirical distributions for the microwave system observations under each hypothesis. Microwave detection is then performed. Instead of trying to recover a complete dielectric image of the breast from the microwave scan, the question of interest in this approach is simply which hypothesis is more consistent with the observed electromagnetic response of the microwave system. A hypothesis testing method based on the likelihood ratio for the empirical distributions and Receiver Operating Characteristic (ROC) optimization is proposed. The results from a simple idealized test case show good potential and invite further study.