In any interconnected healthcare system (e.g., those that are part of a smart city), interactions between patients, medical doctors, nurses and other healthcare practitioners need to be secure and efficient. For example, all members must be authenticated and securely interconnected to minimize security and privacy breaches from within a given network. However, introducing security and privacy-preserving solutions can also incur delays in processing and other related services, potentially threatening patients lives in critical situations. A considerable number of authentication and security systems presented in the literature are centralized, and frequently need to rely on some secure and trusted third-party entity to facilitate secure communications. This, in turn, increases the time required for authentication and decreases throughput due to known overhead, for patients and inter-hospital communications. In this paper, we propose a novel decentralized authentication of patients in a distributed hospital network, by leveraging blockchain. Our notion of a healthcare setting includes patients and allied health professionals (medical doctors, nurses, technicians, etc), and the health information of patients. Findings from our in-depth simulations demonstrate the potential utility of the proposed architecture. For example, it is shown that the proposed architecture's decentralized authentication among a distributed affiliated hospital network does not require re-authentication. This improvement will have a considerable impact on increasing throughput, reducing overhead, improving response time, and decreasing energy consumption in the network. We also provide a comparative analysis of our model in relation to a base model of the network without blockchain to show the overall effectiveness of our proposed solution.