  We develop a systematic theory of symmetry fractionalization for fermionic
topological phases of matter in (2+1)D with a general fermionic symmetry group
$G_f$. In general $G_f$ is a central extension of the bosonic symmetry group
$G_b$ by fermion parity, $(-1)^F$, characterized by a non-trivial cohomology
class $[\omega_2] \in \mathcal{H}^2(G_b, \mathbb{Z}_2)$. We show how the
presence of local fermions places a number of constraints on the algebraic data
that defines the action of the symmetry on the super-modular tensor category
that characterizes the anyon content. We find two separate obstructions to
defining symmetry fractionalization, which we refer to as the bosonic and
fermionic symmetry localization obstructions. The former is valued in
$\mathcal{H}^3(G_b, K(\mathcal{C}))$, while the latter is valued in either
$\mathcal{H}^3(G_b,\mathcal{A}/\{1,\psi\})$ or $Z^2(G_b, \mathbb{Z}_2)$
depending on additional details of the theory. $K(\mathcal{C})$ is the Abelian
group of functions from anyons to $\mathrm{U}(1)$ phases obeying the fusion
rules, $\mathcal{A}$ is the Abelian group defined by fusion of Abelian anyons,
and $\psi$ is the fermion. When these obstructions vanish, we show that
distinct symmetry fractionalization patterns form a torsor over
$\mathcal{H}^2(G_b, \mathcal{A}/\{1,\psi\})$. We study a number of examples in
detail; in particular we provide a characterization of fermionic Kramers
degeneracy arising in symmetry class DIII within this general framework, and we
discuss fractional quantum Hall and $\mathbb{Z}_2$ quantum spin liquid states
of electrons.
