  We analyse a possible connection between CP violations in the quark and
lepton sectors, parametrised by the CKM and PMNS phases. If one assumes that CP
breaking arises from complex Yukawa couplings, both in the quark and lepton
sectors, the above connection is not possible in general, since Yukawa
couplings in the two sectors have independent flavour structures. We show that
both the CKM and PMNS phases can instead be generated by a vacuum phase in a
class of two Higgs doublet models, and in this case a connection may be
established. This scenario requires the presence of scalar FCNC at tree level,
both in the quark and lepton sectors. The appearance of these FCNC is an
obstacle and a blessing. An obstacle since one has to analyse which models are
able to conform to the strict experimental limits on FCNC, both in the quark
and lepton sectors. A blessing, because this class of models is falsifiable
since FCNC arise at a level which can be probed experimentally in the near
future, specially in the processes $h\to e^\pm\tau^\mp$ and $t\to h c$. The
connection between CP violations in CKM and PMNS is explicitely illustrated in
models with Minimal Flavour Violation.
