In this paper, we consider abnormality detection via diffusive molecular communications (MCs) for a network consisting of several sensors and a fusion center (FC). If a sensor detects an abnormality, it injects into the medium a number of molecules which is proportional to the sensed value. Two transmission schemes for releasing molecules into the medium are considered. In the first scheme, referred to as DTM, each sensor releases a different type of molecule, whereas in the second scheme, referred to as STM, all sensors release the same type of molecule. The molecules released by the sensors propagate through the MC channel and some may reach the FC where the final decision regarding whether or not an abnormality has occurred is made. We derive the optimal decision rules for both DTM and STM. However, the optimal detectors entail high computational complexity as log-likelihood ratios (LLRs) have to be computed. To overcome this issue, we show that the optimal decision rule for STM can be transformed into an equivalent low-complexity decision rule. Since a similar transformation is not possible for DTM, we propose simple low-complexity sub-optimal detectors based on different approximations of the LLR. The proposed low-complexity detectors are more suitable for practical MC systems than the original complex optimal decision rule, particularly when the FC is a nano-machine with limited computational capabilities. Furthermore, we analyze the performance of the proposed detectors in terms of their false alarm and missed detection probabilities. Simulation results verify our analytical derivations and reveal interesting insights regarding the trade-off between complexity and performance of the proposed detectors and the considered DTM and STM schemes.