Extra Higgs states appear in various scenarios beyond the current Standard Model of elementary particles. If discovered at the LHC or future colliders, the question will arise whether CP is violated or conserved in the extended scalar sector. An unambiguous probe of (indirect) CP violation would be the observation that one of the extra Higgs particles is an admixture of a CP-even and a CP-odd state. We discuss the possibility to discover scalar CP violation in this way at the high-luminosity (HL) phase of the LHC. We focus on the Two-Higgs Doublet Model of type I, where we investigate its currently allowed parameter region. Considering a benchmark point that is compatible with the current constraints but within reach of the HL-LHC, we study the prospects of determining the CP property of an extra neutral Higgs state $H$ via the angular distribution of final states in the decay $H \to \tau\bar\tau$. The analysis is performed at the reconstructed level, making use of a Boosted Decision Tree for efficient signal-background separation and a shape analysis for rejecting a purely CP-even or odd nature of $H$.