  We investigate methods to explore the CP nature of the $ t\bar{t}h $ coupling
at the LHC, focusing on associated production of the Higgs with a $t \bar{t}$
pair. We first discuss the constraints implied by low-energy observables and by
the Higgs-rate information from available LHC data, emphasizing that they
cannot provide conclusive evidence on the nature of this coupling. We then
investigate kinematic observables that could probe the $ t\bar{t}h $ coupling
directly, in particular quantities that can be constructed out of just
lab-frame kinematics. We define one such observable by exploiting the fact that
$t \bar{t}$ spin correlations do also carry information about the CP-nature of
the $ t\bar{t}h $ coupling. Finally, we introduce a CP-odd quantity and a
related asymmetry, able to probe CP violation in the $ t\bar{t}h $ coupling and
likewise constructed out of lab-frame momenta only.
