  Using an ansatz wave function for the ground state of rotating
two-dimensional dipolar fermions, which occupy only partially the lowest Landau
level, we study the correlation energy and elastic properties of the Wigner
crystal of rotating dipolar Fermi gases. From a simple Hartree-Fock approach,
we show that the correlation energy of a particle crystal is lower and higher
than the correlation energy of a hole crystal for filling factors v<1/2 and
v>1/2, respectively. Furthermore we find that the shear moduli of these dipolar
crystals have a nonmonotonic behavior as a function of the filling factor. We
also examine the stability of a Wigner crystal. The Wigner crystal with the
sample width being zero is locally stable for 0< v <1/2, while the
corresponding hole crystal is locally stable for 1/2< v <1. Due to the WC being
unstable around v=1/2, we also conclude that a new liquid state, not a quantum
Hall state, can exist at v=1/2.
