Different from the traditional healthcare field, Medical Cyber Physical Systems (MCPS) rely more on wireless wearable devices and medical applications to provide better medical services. The secure storage and sharing of medical data are facing great challenges. Blockchain technology with decentralization, security, credibility and tamper-proof is an effective way to solve this problem. However, capacity limitation is one of the main reasons affecting the improvement of blockchain performance. Certificateless aggregation signature schemes can greatly tackle the difficulty of blockchain expansion. In this paper, we describe a two-layer system model in which medical records are stored off-blockchain and shared on-blockchain. Furthermore, a multi-trapdoor hash function is proposed. Based on the proposed multi-trapdoor hash function, we present a certificateless aggregate signature scheme for blockchain-based MCPS. The purpose is to realize the authentication of related medical staffs, medical equipment, and medical apps, ensure the integrity of medical records, and support the secure storage and sharing of medical information. The proposed scheme is highly computationally efficient because it does not use bilinear maps and exponential operations. Many certificateless aggregate signature schemes without bilinear maps in Internet of things (IoT) have been proposed in recent years, but they are not applied to the medical field, and they do not consider the security requirements of medical data. The proposed scheme in this paper has high computing and storage efficiency, while meeting the security requirements in MCPS.