  In the Standard Model, the Higgs boson is a CP even state with CP conserving
couplings; any deviations from this would be a sign of new physics. These CP
properties can be probed by measuring Higgs decays to tau lepton pairs: the
transverse correlation between the tau spins depends on CP. This paper develops
such an analysis, using full simulation of signal and background events in the
International Large Detector concept for the International Linear Collider. We
consider Higgs-strahlung events e+ e- -> Z H) in which the Z boson decays to
electrons, muons, or hadrons, and the Higgs boson decays to $\tau$ leptons,
which then decay either to (pi+ nu) or (pi+ pi0 nu). Assuming 2 ab^{-1} of
integrated luminosity at a center-of-mass energy of 250~GeV, the mixing angle
psi_CP between even and odd CP components of the tau pair from Higgs boson
decays can be measured to a precision of 75~mrad (4.3 deg).
