The paper proposes a decentralized state estimation method for the control of network systems, where a cooperative objective has to be achieved. The nodes of the network are partitioned into independent nodes, providing the control inputs, and dependent nodes, controlled by local interaction laws. The proposed state estimation algorithm allows the independent nodes to estimate the state of the dependent nodes in a completely decentralized way. To do that, it is necessary for each independent node of the network to estimate the control input components computed by the other independent nodes, without requiring communication among the independent nodes. The decentralized state estimator, including an input estimator, is developed and the convergence properties are studied. Simulation results show the effectiveness of the proposed approach.