The Nappi-Witten model is a Wess-Zumino-Witten in which the target space nonreductive Heisenberg group $H_4$. We consider representation theory underlying this conformal field theory. Specifically, we study category of weight modules, with finite-dimensional spaces, over associated affine vertex operator algebra $\mathsf{H}_4$. In particular, classify irreducible $\mathsf{H}_4$-modules and comp...