  At the LHC the CP properties of the top-quark Yukawa interaction can be
probed through Higgs production in gluon fusion or in association with top
quarks. We consider the possibility for both CP-even and CP-odd couplings to
the top quark to be present, and study CP-sensitive observables at
next-to-leading order (NLO) in QCD, including parton-shower effects. We show
that the inclusion of NLO corrections sizeably reduces the theoretical
uncertainties, and confirm that di-jet correlations in $H+2$ jet production
through gluon fusion and correlations of the top-quark decay products in $t\bar
tH$ production can provide sensitive probes of the CP nature of the Higgs
interactions.
