We present new constraints on the rest-frame sound speed, c_eff², and the viscosity parameter, c_vis², of the Cosmic Neutrino Background from the recent measurements of the Cosmic Microwave Background anisotropies provided by the Planck satellite. While broadly consistent with the expectations of c_eff²=c_vis²=1/3 in the standard scenario, the Planck dataset hints for a higher value of the viscosity parameter, with c_vis²=0.60±0.18 at 68% c.l., and a lower value of the sound speed, with c_eff²=0.304±0.013 at 68% c.l. We find a correlation between the neutrino parameters and the lensing amplitude of the temperature power spectrum A_L. When the latter parameter is allowed to vary, we find a better consistency with the standard model with c_vis²=0.51±0.22, c_eff²=0.311±0.019 and A_L=1.08±0.18 at 68% c.l. This result indicates that the anomalous large value of A_L measured by Planck could be connected to non-standard neutrino properties.