  The Gravitational Wave (GW) event GW 170817 was generated by the coalescence
of two neutron stars (NS) and produced an electromagnetic transient, labelled
AT 2017gfo, that was target of a massive observational campaign. Polarimetry, a
powerful diagnostic tool for probing the geometry and emission processes of
unresolved sources, was obtained for this event. The observed linear
polarization was consistent with being mostly induced by intervening dust,
suggesting that the intrinsic emission was weakly polarized ($P < 0.4-0.5$ %).
In this paper, we present and discuss a detailed analysis of the linear
polarization expected from a merging NS binary system by means of 3D Monte
Carlo radiative transfer simulations assuming a range of possible
configurations, wavelengths, epochs and viewing angles. We find that
polarization originates from the non-homogeneous opacity distribution within
the ejecta and can reach levels of $P\sim1$ % at early times (1$-$2 days after
the merger) and in the optical R band. Smaller polarization signals are
expected at later epochs and/or different wavelengths. From the viewing-angle
dependence of the polarimetric signal, we constrain the observer orientation of
AT 2017gfo within $\sim$65$^\circ$ from the polar direction. The detection of
non-zero polarization in future events will unambiguously reveal the presence
of a lanthanide-free ejecta component and unveil its spatial and angular
distribution.
