tau tau decay > We show how the transverse tau tau spin correlations can be
 used  to measure the parity of the Higgs boson  and hence to
 distinguish a CP-even H boson from CP-odd A
 in the future high energy accelerator experiments. We  investigate
 the subsequent decays of the tau into pi nu and rho nu.
 The prospects for the measurement of the Higgs boson parity with a mass
 of 120 GeV are quantified for the case of e+ e- collisions of
 500 GeV center of mass energy.  The Standard Model Higgsstrahlung
 production process is used as an example.