A new censoring approach is proposed to reduce communication costs in distributed sensor networks (SNs) where probability density functions (PDFs) are transmitted to a fusion center (FC). In the approach, at each time step, each sensor will collect new measurement data, and based on its local state posterior PDF and its knowledge about other sensors’ measurement models, compute the expected value of the Kullback-Leibler divergence (KLD) between the global prior and global posterior obtained by fusing a subset of local posteriors, for all the possible subsets. Each sensor will then send the index of the subset of sensors corresponding to the highest expected KLD to the FC. The FC will then request the full posterior data from each sensor in the subset with the highest number of votes. A Monte Carlo (MC) approximation is proposed to evaluate the expected KLD. Numerical results for a radar SN tracking example are provided to demonstrate the utility of the proposed method.