With the generation of personal and medical data at several locations, medical data science faces unique challenges when working on distributed datasets. Growing data protection requirements in recent years drastically limit the use of personally identifiable information. Distributed data analysis aims to provide solutions for securely working on highly sensitive data while minimizing the risk of information leaks, which would not be possible to the same degree in a centralized approach. A novel concept in this field is the Personal Health Train (PHT), which encapsulates the idea of bringing the analysis to the data, not vice versa. Data sources are represented as train stations. Trains containing analysis tasks move between stations and aggregate results. Train executions are coordinated by a central station which data analysts can interact with. Data remains at their respective stations and analysis results are only stored inside the train, providing a safe and secure environment for distributed data analysis. Duplicate records across multiple locations can skew results in a distributed data analysis. On the other hand, merging information from several datasets referring to the same real-world entities may improve data completeness and therefore data quality. In this paper, we present an approach for record linkage on distributed datasets using the Personal Health Train. We verify this approach and evaluate its effectiveness by applying it to two datasets based on real-world data and outline its possible applications in the context of distributed data analysis tasks.