This thesis presents a study of the CP properties of the Standard Model (SM) Higgs boson interaction with τ leptons. In those SM interactions the CP symmetry is conserved. The measurement of the properties is performed by defning a CP sensitive angular observable ϕ∗CP , which can be kinematically constructed from the Higgs visible decay products. The interactions occurring between the SM Higgs particle and the τ particles are described by making use of a mixing angle φτ appearing in the Yukawa coupling. The two channels considered in the thesis are the τhadτhad and the τlepτhad channels, where τhad denotes a hadronic decay of the τ and τlep denotes a leptonic τ decay. The study is performed using proton-proton collision data recorded between 2015 and 2018 with the ATLAS detector at the Large Hadron Collider. The measured (expected) φτ value is equal to 8.68◦ ± 16◦ (0 ◦ ± 28◦ ) at the 68% condence level (CL), and 8.68◦ ± 34◦ (−70◦/ + 75◦ ) at the 95.5% CL. The pure CP-odd hypothesis is rejected at a value of 3.4σ (standard deviation), which implies a compatibility between the measurement and the Higgs prediction in the Standard Model.