  By computing anomalous dimensions of gauge invariant composite operators
$(\bar\psi\psi)^n$ and $(\phi^*\phi)^n$ in Chern-Simons fermion and boson
models, we address that Chern-Simons interactions make these operators more
relevant or less irrelevant in the low energy region. We obtain a critical
Chern-Simons fermion coupling, ${1\over \kappa_c^2} = {6\over 19}$, for a phase
transition at which the leading irrelevant four-fermion operator
$(\bar\psi\psi)^2$ becomes marginal, and a critical Chern-Simons boson
coupling, ${1\over \kappa_c^2} = {6\over 34}$, for a similar phase transition
for the leading irrelevant operator $(\phi^*\phi)^4$. We see this phenomenon
also in the $1/N$ expansion.
