  A multi-messenger, black hole (BH) - neutron star (NS) merger event still
remains to be detected. The tidal (dynamical) ejecta from such an event,
thought to produce a kinonova, is concentrated in the equatorial plane and
occupies only part of the whole azimuthal angle. In addition, recent
simulations suggest that the outflow or wind from the post-merger remnant disk,
presumably anisotropic, can be a major ejecta component responsible for a
kilonova. For any ejecta whose photosphere shape deviates from the spherical
symmetry, the electron scattering at the photosphere causes a net polarization
in the kilonova light. Recent observational and theoretical polarization
studies have been focused to the NS-NS merger kilonova AT2017gfo. We extend
those work to the case of a BH-NS merger kilonova. We show that the degree of
polarization at the first $\sim 1$ hr can be up to $\sim$ 3\% if a small amount
($10^{-4} M_{\odot}$) of free neutrons have survived in the fastest component
of the dynamical ejecta, whose beta-decay causes a precursor in the kilonova
light. The polarization degree can be $\sim$ 0.6\% if free neutrons survived in
the fastest component of the disk wind. Future polarization detection of a
kilonova will constrain the morphology and composition of the dominant ejecta
component, therefore help to identify the nature of the merger.
