Abstract: A study of the charge conjugation and parity (CP) properties of the interaction between the Higgs boson and tau -leptons is presented. The study is based on a measurement of CP-sensitive angular observables defined by the visible decay products of t -leptons produced in Higgs boson decays. The analysis uses 139 fb(-1) of proton-proton collision data recorded at a centre-of-mass energy of root s = 13 TeV with the ATLAS detector at the Large Hadron Collider. Contributions from CP-violating interactions between the Higgs boson and t -leptons are described by a single mixing angle parameter phi(tau) in the generalised Yukawa interaction. Without constraining the H -> tau tau signal strength to its expected value under the Standard Model hypothesis, the mixing angle ft is measured to be 9 degrees +/- 16 degrees, with an expected value of 0 degrees +/- 28 degrees at the 68% confidence level. The pure CPodd hypothesis is disfavoured at a level of 3.4 standard deviations. The results are compatible with the predictions for the Higgs boson in the Standard Model.