  We note that in (2+1)-dimensional gauge theories with even number of massless
fermions, there is anomalous $Z_2$ symmetry if theory is regularized in a
parity-invariant way. We then consider a parity invariant $U(1)_V\times U(1)_A$
model, which induces a mutual Chern-Simons term in the effective action due to
$Z_2$ anomaly. The effect of the discrete anomaly is studied in the induced
spin and in the dynamical fermion mass.
