  The Hopf term in the $2 + 1$ dimensional O(3) nonlinear sigma model, which is
known to be responsible for fractional spin and statistics, is re-examined from
the viewpoint of quantization ambiguity. It is confirmed that the Hopf term can
be understood as a term induced quantum mechanically, in precisely the same
manner as the $\theta$-term in QCD. We present a detailed analysis of the
topological aspect of the model based on the adjoint orbit parametrization of
the spin vectors, which is not only very useful in handling topological
(soliton and/or Hopf) numbers, but also plays a crucial role in defining the
Hopf term for configurations of nonvanishing soliton numbers. The Hopf term is
seen to arise explicitly as a quantum effect which emerges when quantizing an
$S^1$ degree of freedom hidden in the configuration space.
