Perspectives for a measurement of the tau lepton polarization in $Z\to\tau \tau$ decays with the CMS experiment

The potential of the CMS detector to measure the $\tau$ lepton polarization asymmetry in $Z^0$ decays is studied. Using data corresponding to an integrated luminosity of 19.6 fb$^{-1}$ at 8 TeV and 2.3 fb$^{-1}$ at 13 TeV the $\tau$ polarization asymmetry is measured exploiting decay channels $\tau\to\rho\nu$ and $\tau\to a_1\nu$