  The two-Higgs-doublet model can be constrained by imposing Higgs-family
symmetries and/or generalized CP symmetries. It is known that there are only
six independent classes of such symmetry-constrained models. We study the CP
properties of all cases in the bilinear formalism. An exact symmetry implies CP
conservation. We show that soft breaking of the symmetry can lead to
spontaneous CP violation (CPV) in three of the classes.
