  We provide a mathematical proposal for the anomaly indicators of symmetries
of (2+1)-d fermionic topological orders, and work out the consequences of our
proposal in several nontrivial examples. Our proposal is an invariant of a
super modular tensor category with a fermionic group action, which gives a
(3+1)-d topological field theory (TFT) that we conjecture to be invertible; the
anomaly indicators are partition functions of this TFT on $4$-manifolds
generating the corresponding twisted spin bordism group. Our construction
relies on a bosonization construction due to Gaiotto-Kapustin and
Tata-Kobayashi-Bulmash-Barkeshli, together with a ``bosonization conjecture''
which we explain in detail. In the second half of the paper, we discuss several
examples of our invariants relevant to condensed-matter physics. The most
important example we consider is $\mathbb{Z}/4^T\times \mathbb{Z}/2^f$
time-reversal symmetry with symmetry algebra $\mathcal T^2 = (-1)^FC$, which
many fermionic topological orders enjoy, including the $\mathrm{U}(1)_5$ spin
Chern-Simons theory. Using newly developed tools involving the Smith long exact
sequence, we calculate the cobordism group that classifies its anomaly, present
the generating manifold, and calculate the partition function on the generating
manifold which serves as our anomaly indicator. Our approach allows us to
reproduce anomaly indicators known in the literature with simpler proofs,
including $\mathbb{Z}/4^{Tf}$ time-reversal symmetry with symmetry algebra
$\mathcal T^2 = (-1)^F$, and other symmetry groups in the 10-fold way involving
Lie group symmetries.
