  We investigate the effects of the Chern-Simons coupling on the high energy
behavior in the $(2+1)$-dimensional Chern-Simons QED with a four-Fermi
interaction. Using the $1/N$ expansion we discuss the Chern-Simons effects on
the critical four-Fermi coupling at $O(1/N)$ and the $\beta$ function around
it. High-energy behavior of Green's functions is also discussed. By explicit
calculation, we find that the radiative correction to the Chern-Simons coupling
vanishes at $O(1/N)$ in the broken phase of the dynamical parity symmetry. We
argue that no radiative corrections to the Chern-Simons term arise at higher
orders in the $1/N$ expansion.
