  We derive an effective action for Dirac fermions coupled to O(3) non-linear
sigma-model (NLSM) through the Yukawa-type interaction. The nonperturbative
(global) quantum anomaly of this model results in a Hopf term for the effective
NLSM. We obtain this term using the ``embedding'' of the CP$^1$ model into the
CP$^M$ generalization of the model which makes the quantum anomaly
perturbative. This perturbative anomaly is calculated by means of a gradient
expansion of a fermionic determinant and is given by the Chern-Simons term for
an auxiliary gauge field.
