  Recently it was shown by Cho and Kimm that the gauged $CP^1$ model, obtained
by gauging the global $SU(2)$ group and adding a corresponding Chern-Simons
term, has got its own soliton. These solitons are somewhat distinct from those
of pure $CP^1$ model as they cannot always be characterised by $\pi_2(CP^1)=Z$.
In this paper, we first carry out a detailed Hamiltonian analysis of this
gauged $CP^1$ model. This reveals that the model has only $SU(2)$ as the gauge
invariance, rather than $SU(2) \times U(1)$. The $U(1)$ gauge invariance of the
original (ungauged) $CP^1$ model is actually contained in the $SU(2)$ group
itself. Then we couple the Hopf term associated to these solitons and again
carry out its Hamiltonian analysis. The symplectic structures, along with the
structures of the constraints of these two models (with or without Hopf term)
are found to be essentially the same. The model with a Hopf term is shown to
have fractional spin which, when computed in the radiation gauge, is found to
depend not only on the soliton number $N$, but also on the nonabelian charge.
We then carry out a reduced (partially) phase space analysis in a different
physical sector of the model where the degrees of freedom associated with the
$CP^1$ fields are transformed away. The model now reduces to a $U(1)$ gauge
theory with two Chern-Simons gauge fields getting mass-like terms and one
remaining massless. In this case the fractional spin is computed in terms of
the dynamical degrees of freedom and shown to depend purely on the charge of
the surviving abelian symmetry. Although this reduced model is shown to have
its own solitonic configuration, it turns out to be trivial.
