We consider the problem of decentralized Kalman filtering in a sensor network. Each sensor node implements a local Kalman filter based on its own measurements and the information exchanged with its neighbors. It combines the information received from other sensors through using a consensus filter as proposed in [14]. For a time-invariant process and measurement model, we show that this algorithm guarantees that the local estimates of the error covariance matrix converge to the centralized error covariance matrix and that the local estimates of the state converge in mean to the centralized Kalman filter estimates. However, due to the use of the consensus filter, the local estimates of the state do not converge to the least-squares estimate that would be obtained from a centralized Kalman filter.