Local estimation errors are often correlated in distributed estimation fusion. In this paper, we model this correlation and study its effect on fusion performance for a vector-valued estimand (i.e., quantity to be estimated). This correlation is summarily quantified by a generalized correlation coefficient . We model the cross-covariance matrix of the local estimation errors as times a square root of the product of the two local error covariance matrices. Then the dependence of the distributed best linear unbiased estimation (BLUE) fusion on this is analyzed. It is found that in the case of perfect correlation, the BLUE fuser is error free. It is also found that the mean square error (mse) of the fused estimate is concave and has a unique maximum with respect to . Whether negative correlation or positive correlation is better for the BLUE fusion depends on the situation. So does the sign of at which the fusion mse is maximized. Examples illustrating these findings are given.