  We predict linear polarization for a radioactively-powered kilonova following
the merger of a black hole and a neutron star. Specifically, we perform 3-D
Monte Carlo radiative transfer simulations for two different models, both
featuring a lanthanide-rich dynamical ejecta component from
numerical-relativity simulations while only one including an additional
lanthanide-free disk wind component. We calculate polarization spectra for nine
different orientations at 1.5, 2.5 and 3.5 d after the merger and in the
$0.1-2\,\mu$m wavelength range. We find that both models are polarized at a
detectable level 1.5 d after the merger while show negligible levels
thereafter. The polarization spectra of the two models are significantly
different. The model lacking a disk wind shows no polarization in the optical,
while a signal increasing at longer wavelengths and reaching $\sim1\%-6\%$ at
$2\,\mu$m depending on the orientation. The model with a disk-wind component,
instead, features a characteristic "double-peak" polarization spectrum with one
peak in the optical and the other in the infrared. Polarimetric observations of
future events will shed light on the debated neutron richness of the disk-wind
component. The detection of optical polarization would unambiguously reveal the
presence of a lanthanide-free disk-wind component, while polarization
increasing from zero in the optical to a peak in the infrared would suggest a
lanthanide-rich composition for the whole ejecta. Future polarimetric campaigns
should prioritize observations in the first $\sim48$ hours and in the
$0.5-2\,\mu$m range, where polarization is strongest, but also explore shorter
wavelengths/later times where no signal is expected from the kilonova and the
interstellar polarization can be safely estimated.
