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In the framework of spin-0 $s$-channel simplified models, we explore thepossibility of assessing the structure of dark matter interactions through theassociate production of dark matter and $t\bar{t}$ pairs. To this purpose,final states with two leptons are considered and the kinematic properties ofthe dilepton system is studied. We develop a realistic analysis strategy andprovide a detailed evaluation of the achievable sensitivity for the dark mattersignal assuming integrated luminosities of $300 \, {\rm fb}^{-1}$ and $3 \,{\rm ab}^{-1}$ at the 14 TeV LHC. Furthermore, upper limits on the mediatormasses for which the two different CP hypotheses can be distinguished arederived. The obtained limits on the signal strengths are finally translatedinto constraints on the parameter space of two spin-0 simplified modelsincluding a scenario with an extended Higgs sector.

Determining the CP nature of spin-0 mediators in associated production of dark matter and $t \bar t$ pairs