Structural analysis is a useful tool for fault diagnosability analysis to handle systems that are described by a large set of non-linear differential algebraic equations. Distributed fault diagnosis is an attractive approach for complex systems to reduce computational complexity by partitioning the system into a set of smaller subsystems and perform fault diagnosis of each subsystem. Defining these subsystems requires methods to understand how fault diagnosis properties of each subsystem relates to the properties of the whole system. Another related problem is that large and complex systems are likely to be developed by several companies where each company is developing different subsystems that can be used in different system configurations. In these situations, each subsystem will have limited model information about the other subsystems, which complicates performing structural analysis of the whole system. The main contribution in this work is extending some of the existing results in structural analysis for one system model to a distributed set of connected subsystems. The results show the relationship between structural fault diagnosis properties of the whole system and properties of the set of individual subsystems.