This paper studies decentralized estimation with correlated observations. Focusing on the additive model with correlated Gaussian noises, we attempt to answer several distinct yet related questions in decentralized estimation: 1. When does correlation imply redundancy, i.e., incur performance degradation compared with that of independent observations; 2. What is the optimal quantizer structure that maximizes the Fisher information at the fusion center; 3. What is the preferred communication direction in a tandem fusion network involving correlated observations? It is shown that there exist different correlation regimes whose impacts on the estimation performance are in sharp contrast with each other. For the Gaussian model, it is established that quantizing the observation is optimal regardless of the correlation coefficients; this is true despite the fact that subsequent estimators may differ at the fusion center. Finally, it is always beneficial to have the better sensor (i.e., that has a higher SNR) to serve as a fusion center in a tandem fusion network for all correlation regimes.