In this paper, we consider target detection in suspicious tissue via diffusive molecular communications (MCs). If a target is present, it continuously and with a constant rate secretes molecules of a specific type, so-called biomarkers, into the medium, which are symptomatic for the presence of the target. Detection of these biomarkers is challenging since due to the diffusion and degradation, the biomarkers are only detectable in the vicinity of the target. In addition, the exact location of the target within the tissue is not known. In this paper, we propose to distribute several reactive nanosensors (NSs) across the tissue such that at least some of them are expected to come in contact with biomarkers, which cause them to become activated. Upon activation, an NS releases a certain number of molecules of a secondary type into the medium to alert a fusion center (FC), where the final decision regarding the presence of the target is made. In particular, we consider a composite hypothesis testing framework where it is assumed that the location of the target and the biomarker secretion rate are unknown, whereas the locations of the NSs are known. We derive the uniformly most powerful (UMP) test for the detection at the NSs. For the final decision at the FC, we show that the UMP test does not exist. Hence, we derive a genie-aided detector as an upper bound on performance. We then propose two sub-optimal detectors and evaluate their performance via simulations