In this paper, we present the globally optimal distributed Kalman filtering fusion with singular covariances of filtering errors and measurement noises. The following facts motivate us to consider the problem. First, the invertibility of estimation error covariance matrices is a necessary condition for most of the existing distributed fusion algorithms. However, it can not be guaranteed to exist in practice. For example, when state estimation for a given dynamic system is subject to state equality constraints, the estimation error covariance matrices must be singular. Second, the proposed fused state estimate is still exactly the same as the centralized Kalman filtering using all sensor raw measurements. Moreover, the existing performance analysis results on the distributed Kalman filtering fusion for the multisensor system with feedback are also extended to the singular covariance matrices of filtering error. The final numerical examples support the theoretical results and show an advantage of less computational burden.