Autonomous radio-detection, i.e., detection of air-showers with standalone radio arrays, is one of the major technical challenges to overcome for the next generation astroparticle detectors. In this context, we study polarisation signatures of simulated radio signals to perform an identification of the associated air-showers initiated by cosmic-rays and neutrinos. We compare the two sources of radio emission (the charge excess and geomagnetic) and show that the former is almost negligible for inclined (zenith angle $>65°$) cosmic-ray air-showers. This provides an efficient background rejection criterion at the DAQ level, based on the projection of the total electric field along the direction of the local magnetic field. This relevant quantity can be computed, — even in an online treatment — for antennas measuring three orthogonal polarisations. Independently of the experimental antenna layout, we estimate that assuming a random polarisation of noise events, a rejection from $\approx 72\text{\%}$ (for a non favourable detector location) to $\approx 93\text{\%}$ (for a favourable one) of the noise induced events and a trigger efficiency of 86% (93%) with a $3\sigma$ ($5\sigma$) trigger threshold level should be achievable. We also show that neutrino-induced showers present a charge excess to geomagnetic signal ratio up to $\sim 10$ times higher than for cosmic ray showers. Although this characteristic makes the identification of neutrino-induced showers challenging via the method developed here, it provides an efficient criterion to perform an offline discrimination between cosmic-ray and neutrino primaries. The stronger charge excess emission will also help the reconstruction of air-shower parameters, such as the core position.