  The question whether the Higgs boson is connected to additional CP violation
is one of the driving forces behind precision studies at the Large Hadron
Collider. In this work, we investigate the CP structure of the top quark Yukawa
interaction-one of the most prominent places for searching for New
Physics-through Higgs boson loops in top quark pair production. We calculate
the electroweak corrections including arbitrary CP mixtures at
next-to-leading-order in the Standard Model Effective Field Theory. This
approach of probing Higgs boson degrees of freedom relies on the large
$t\bar{t}$ cross section and the excellent perturbative control. In addition,
we consider all direct probes with on-shell Higgs boson production in
association with a single top quark or top quark pair. This allows us to
contrast loop sensitivity versus on-shell sensitivity in these fundamentally
different process dynamics. We find that loop sensitivity in $t\bar{t}$
production and on-shell sensitivity in $t\bar{t}H$ and $tH$ provide
complementary handles over a wide range of parameter space.
