  In an effort to further the study of amplitudes in the celestial CFT (CCFT),
we construct conformal primary wavefunctions for massive fermions. Upon
explicitly calculating the wavefunctions for Dirac fermions, we deduce the
corresponding transformation of momentum space amplitudes to celestial
amplitudes. The shadow wavefunctions are shown to have opposite spin and
conformal dimension $2-\Delta$. The Dirac conformal primary wavefunctions are
delta function normalizable with respect to the Dirac inner product provided
they lie on the principal series with conformal dimension $\Delta = 1+i\lambda$
for $\lambda\in\mathbb{R}$. It is shown that there are two choices of a
complete basis: single spin $J=\frac{1}{2}$ or $J=-\frac{1}{2}$ and
$\lambda\in\mathbb{R}$ or multiple spin $J=\pm\frac{1}{2}$ and
$\lambda\in\mathbb{R}_{+\cup 0}$. The massless limit of the Dirac conformal
primary wavefunctions is shown to agree with previous literature. The momentum
generators on the celestial sphere are derived and, along with the Lorentz
generators, form a representation of the Poincare algebra. Finally, we show
that the massive spin-$1$ conformal primary wavefunctions can be constructed
from the Dirac conformal primary wavefunctions using the standard
Clebsch-Gordan coefficients. We use this procedure to write the massive
spin-$\frac{3}{2}$, Rarita-Schwinger, conformal primary wavefunctions. This
provides a prescription for constructing all massive fermionic and bosonic
conformal primary wavefunctions starting from spin-$\frac{1}{2}$.
