  In this short paper, we argue that the chiral central charge $c_-$ of a
(2+1)d topological ordered state is sometimes strongly constrained by 't Hooft
anomaly of anti-unitary global symmetry. For example, if a (2+1)d fermionic
TQFT has a time reversal anomaly with $T^2=(-1)^F$ labeled as
$\nu\in\mathbb{Z}_{16}$, the TQFT must have $c_-=1/4$ mod $1/2$ for odd $\nu$,
while $c_-=0$ mod $1/2$ for even $\nu$. This generalizes the fact that the
bosonic TQFT with $T$ anomaly in a particular class must carry $c_-=4$ mod $8$
to fermionic cases. We also study such a constraint for fermionic TQFT with
$U(1)\times CT$ symmetry, which is regarded as a gapped surface of the
topological superconductor in class AIII.
