  We find an intriguing relation between a class of 3-dimensional non-unitary
topological field theories (TFTs) and Virasoro minimal models $M(2,2r+3)$ with
$r \geq 1$. The TFTs are constructed by topologically twisting $3d$ ${\mathcal
N}=4$ superconformal field theories (SCFTs) of rank-0, i.e. having
zero-dimensional Coulomb and Higgs branches. We present ultraviolet (UV) field
theory descriptions of the SCFTs with manifest ${\mathcal N}=2$ supersymmetry,
which we argue is enhanced to ${\mathcal N}=4$ in the infrared. From the UV
description, we compute various partition functions of the TFTs and reproduce
some basic properties of the minimal models, such as their characters and
modular matrices. We expect more general correspondence between topologically
twisted $3d$ ${\mathcal N}=4$ rank-0 SCFTs and $2d$ non-unitary rational
conformal field theories.
