Fermionic symmetry fractionalization in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math> dimensions

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