Equivalent dual theories for 3D $\mathcal{N}=2$ supergravity

$\mathcal{N}=2$ three-dimensional supergravity with internal $R$-symmetry generators can be understood as a two-dimensional chiral Wess-Zumino-Witten model. In this paper, we present the reduced phase space description of the theory, which turns out to be a flat limit of a generalized Liouville theory, up to zero modes. The reduced phase space description can also be explained as a gauged chiral Wess-Zumino-Witten model. We show that both these descriptions possess identical gauge and global (quantum $\mathcal{N}=2$ super ${\mathrm{BMS}}_3$) symmetries.