NLO QCD corrections and off-shell effects for $t\bar{t}H$ production in the Higgs characterisation model

In these proceedings we discuss $t\bar{t}H$ production at the Large Hadron Collider in the Higgs characterisation model. We demonstrate the importance of off-shell effects and higher-order QCD corrections for this process and highlight the importance of single-resonant contributions for the production of a $\mathcal{C}\mathcal{P}$-odd Higgs boson.