In modern hospitals, patients are treated using a wide array of medical devices that are increasingly interacting with each other over the network, thus offering a perfect example of a cyber-physical system. We study the safety of a medical device system for the physiologic closed-loop control of drug infusion. The main contribution of the paper is the verification approach for the safety properties of closed-loop medical device systems. We demonstrate, using a case study, that the approach can be applied to a system of clinical importance. Our method combines simulation-based analysis of a detailed model of the system that contains continuous patient dynamics with model checking of a more abstract timed automata model. We show that the relationship between the two models preserves the crucial aspect of the timing behavior that ensures the conservativeness of the safety analysis. We also describe system design that can provide open-loop safety under network failures.