This paper extends the results of [13] on distributed state predictions to state filtering for a networked system. An observer is constructed which has a structure similar to that of the plant, and a recursive formula is derived for its optimal update gain matrix. This estimator inherits almost all advantages of the one-step predictor, which include that it utilizes only local system output measurements which is attractive in realizing it in a distributed way, computational complexity increases only quadratically with the subsystem number that makes it simply scalable to a large scale system. It has also been made clear that when estimation error variances are adopted in performance comparisons, the optimal gain matrix is usually unique. A recursive expression is also derived for the covariance matrix of estimation errors. Numerical simulation results show that the suggested distributed state estimator may be as precise as the lumped Kalman filter.