jats:titleAbstract</jats:title>jats:pA study of the charge conjugation and parity (jats:inline-formulajats:alternativesjats:tex-math$$\textit{CP}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:miCP</mml:mi> </mml:math></jats:alternatives></jats:inline-formula>) properties of the interaction between the Higgs boson and jats:inline-formulajats:alternativesjats:tex-math$$\tau $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:miτ</mml:mi> </mml:math></jats:alternatives></jats:inline-formula>-leptons is presented. The study is based on a measurement of jats:inline-formulajats:alternativesjats:tex-math$$\textit{CP}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:miCP</mml:mi> </mml:math></jats:alternatives></jats:inline-formula>-sensitive angular observables defined by the visible decay products of jats:inline-formulajats:alternativesjats:tex-math$$\tau $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:miτ</mml:mi> </mml:math></jats:alternatives></jats:inline-formula>-leptons produced in Higgs boson decays. The analysis uses 139 fbjats:inline-formulajats:alternativesjats:tex-math$$^{-1}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:msup mml:mrow/ mml:mrow mml:mo-</mml:mo> mml:mn1</mml:mn> </mml:mrow> </mml:msup> </mml:math></jats:alternatives></jats:inline-formula> of proton–proton collision data recorded at a centre-of-mass energy of jats:inline-formulajats:alternativesjats:tex-math$$\sqrt{s}= 13$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mrow mml:msqrt mml:mis</mml:mi> </mml:msqrt> mml:mo=</mml:mo> mml:mn13</mml:mn> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> TeV with the ATLAS detector at the Large Hadron Collider. Contributions from jats:inline-formulajats:alternativesjats:tex-math$$\textit{CP}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:miCP</mml:mi> </mml:math></jats:alternatives></jats:inline-formula>-violating interactions between the Higgs boson and jats:inline-formulajats:alternativesjats:tex-math$$\tau $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:miτ</mml:mi> </mml:math></jats:alternatives></jats:inline-formula>-leptons are described by a single mixing angle parameter jats:inline-formulajats:alternativesjats:tex-math$$\phi _{\tau }$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:msub mml:miϕ</mml:mi> mml:miτ</mml:mi> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> in the generalised Yukawa interaction. Without constraining the jats:inline-formulajats:alternativesjats:tex-math$$H\rightarrow \tau \tau $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mrow mml:miH</mml:mi> mml:mo→</mml:mo> mml:miτ</mml:mi> mml:miτ</mml:mi> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> signal strength to its expected value under the Standard Model hypothesis, the mixing angle jats:inline-formulajats:alternativesjats:tex-math$$\phi _{\tau }$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:msub mml:miϕ</mml:mi> mml:miτ</mml:mi> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> is measured to be jats:inline-formulajats:alternativesjats:tex-math$$9^{\circ } \pm 16^{\circ }$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mrow mml:msup mml:mn9</mml:mn> mml:mo∘</mml:mo> </mml:msup> mml:mo±</mml:mo> mml:msup mml:mn16</mml:mn> mml:mo∘</mml:mo> </mml:msup> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula>, with an expected value of jats:inline-formulajats:alternativesjats:tex-math$$0^{\circ } \pm 28^{\circ }$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mrow mml:msup mml:mn0</mml:mn> mml:mo∘</mml:mo> </mml:msup> mml:mo±</mml:mo> mml:msup mml:mn28</mml:mn> mml:mo∘</mml:mo> </mml:msup> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> at the 68% confidence level. The pure jats:inline-formulajats:alternativesjats:tex-math$$\textit{CP}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:miCP</mml:mi> </mml:math></jats:alternatives></jats:inline-formula>-odd 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.</jats:p>