  A super-modular category is a unitary pre-modular category with M\"uger
center equivalent to the symmetric unitary category of super-vector spaces.
Super-modular categories are important alternatives to modular categories as
any unitary pre-modular category is the equivariantization of a either a
modular or super-modular category. Physically, super-modular categories
describe universal properties of quasiparticles in fermionic topological phases
of matter. In general one does not have a representation of the modular group
$\mathrm{SL}(2,\mathbb{Z})$ associated to a super-modular category, but it is
possible to obtain a representation of the (index 3) $\theta$-subgroup:
$\Gamma_\theta<\mathrm{SL}(2,\mathbb{Z})$. We study the image of this
representation and conjecture a super-modular analogue of the Ng-Schauenburg
Congruence Subgroup Theorem for modular categories, namely that the kernel of
the $\Gamma_\theta$ representation is a congruence subgroup. We prove this
conjecture for any super-modular category that is a subcategory of modular
category of twice its dimension, i.e. admitting a minimal modular extension.
Conjecturally, every super-modular category admits (precisely 16) minimal
modular extensions and, therefore, our conjecture would be a consequence.
