  In many exoplanetary systems with `hot Jupiters', it is observed that the
spin axes of host stars are highly misaligned to planetary orbital axes. In
this study, a possible channel is investigated for producing such a
misalignment under a hierarchical three-body system where the evolution of
stellar spin is subjected to the gravitational torque induced from the planet
inside Kozai--Lidov (KL) resonance. In particular, two special configurations
are explored in detail. The first one corresponds to the configuration with
planets at KL fixed points, and the second one corresponds to the
configurations with planets moving on KL librating cycles. When the planet is
located at the KL fixed point, the corresponding Hamiltonian model is of one
degree of freedom and there are three branches of libration centres for stellar
spin. When the planet is moving on KL cycles, the technique of Poincar\'e
section is taken to reveal global structures of stellar spin in phase space. To
understand the complex structures, perturbative treatments are adopted to study
rotational dynamics. It shows that analytical structures in phase portraits
under the resonant model can agree well with numerical structures arising in
Poincar\'e sections, showing that the complicated dynamics of stellar spin are
governed by the primary resonance under the unperturbed Hamiltonian model in
combination with the 2:1 (high-order and/or secondary) spin-orbit resonances.
