In this paper, we present a procedure for the state estimation and fault diagnosis of a labeled Time Petri net system. Starting from the State Class Graph defined by Berthomieu and Diaz, we introduce a new graph called Modified State Class Graph (MSCG) that allows an exhaustive representation of the evolution of the timed system. Then, we present a procedure that, given a timed observation, i.e., a sequence of labels with their firing time instants, and a time instant tau, allows one to determine in which states the system can be at time tau by using the MSCG and solving a certain number of linear programming problems. Finally, we present a procedure to perform fault diagnosis using the MSCG.