In this paper, we propose a novel distributed fault detection method to monitor the state of a linear system, partitioned into interconnected subsystems. The approach hinges on the definition of a partition-based distributed Luenberger estimator, based on the local model of the subsystems and that takes into account the dynamic coupling terms between the subsystems. The proposed methodology computes – in a distributed way – a bound on the variance of a properly defined residual signal, considering the uncertainty related to the state estimates performed by the neighboring subsystems. This bound allows the computation of suitable local thresholds with guaranteed maximum false-alarms rate. The implementation of the proposed estimation and fault detection method is scalable, allowing Plug & Play operations and the possibility to disconnect the faulty subsystem after fault detection. Theoretical conditions guaranteeing the convergence of the estimates and of the bounds are provided. Simulation results show the effectiveness of the proposed method.