Large-scale distributed energy resources (DERs) in the form of DC source load access to the DC distribution network. The probability and correlation of DERs power are remarkable, which profoundly affects the accuracy of the DC distribution network situational awareness with insufficient real-time measurement data and pseudo-measurement data-dependent. It is an urgent need to study the optimal placement of real-time measurement points to ensure the accuracy of system state estimation (SE). Therefore, a pseudo-measurement model of node injected power considering the impact of probability and correlation of source-load power is firstly established in this paper. And a stochastic state estimation (SSE) method for DC distribution network based on the modified Nataf transformation with the three-point estimation is proposed, and the probability distribution of the node voltage estimation deviation can be calculated. On this basis, a stochastic optimal placement model of measurement for DC distribution network considering the chance constraint of the node voltage estimation deviation is built to minimize the measurement placement cost, and the optimal placement scheme can be figured out. The modified IEEE-33 node system is used to carry out case simulation, and the results show that the proposed method can effectively balance the economy of measurement placement and the SE accuracy.