The complete split graph $S_{m,n}$ is a bipartite graph with two parts, a clique part with $m$ vertices which induces $K_m$ as a subgraph, and an independent part with $m$ vertices which induces an empty subgraph $\overline{K_n}$ as a subgraph. There are exactly one edge between each vertex in the clique part and each vertex in the independent part. In this paper, we first determine resistance distances in the vertex-weighted complete split graph $S_{m,n}^\omega$. We also obtain the moon type formula for the vertex-weighted complete split graph $S_{m,n}$, that is, the weighted spanning tree enumerator of $S_{m,n}^\omega$ containing any fixed spanning forest.