  The process $e^- e^+ \to \tau^- \tau^+$ is of particular interest because the
tau lepton polarisation can be reconstructed, allowing its chiral nature to be
probed. This note reports on a study of the reconstruction of the di-tau final
state at ILC-500, its selection and the reduction of backgrounds, the
identification of the tau lepton's decay mode, and on the extraction of the tau
leptons' polarisation. The performance of this analysis is studied in two
models of the ILD detector, one larger (IDR-L) the other smaller (IDR-S), which
differ in the outer radius of the TPC and of the subdetectors beyond, and in
the magnetic field strength of the detector solenoid. We find that the
high-mass tau-pair events in which at least one tau decays haronically can be
selected with an efficiency of around 60%, with a remaining background from
non-di-tau processes at the few-% level. Single-prong decay modes $\tau^\pm \to
\pi^\pm \nu, \tau^\pm \to \pi^\pm \pi^0 \nu, \tau^\pm \to \pi^\pm \pi^0 \pi^0
\nu$ can be correctly identified in around 60-90% of cases, with sample
purities in the range 50-90%, depending on decay mode. The sensitivity to tau
polarisation was estimated in the four beam polarisation datasets envisaged for
the $4\ ab^{-1}$ of data forseen for ILC-500. Statistical precisions on the
polarisation in the different datasets are predicted to be between 0.5 and 2%.
While some small performance differences between the two detector models are
seen, they have very similar final sensitivity to the polarisation measurement.
