  It is important to provide guidance on whether CP violation may be measurable
in top-quark production at the Large Hadron Collider. The present work extends
an earlier analysis of the non-supersymmetric Two-Higgs-Doublet Model in this
respect, by allowing a more general potential. Also, a more comprehensive study
of theoretical and experimental constraints on the model is presented. Vacuum
stability, unitarity, direct searches and electroweak precision measurements
severely constrain the model. We explore, at low \tan\beta, the allowed regions
in the multidimensional parameter space that give a viable physical model. This
exploration is focused on the parameter space of the neutral sector rotation
matrix, which is closely related to the Yukawa couplings of interest. In most
of the remaining allowed regions, the model violates CP. We present a
quantitative discussion of a particular CP-violating observable. This would be
measurable in semileptonically decaying top and antitop quarks produced at the
LHC, provided the number of available events is of the order of a million.
