  In Type-I seesaw model, the lepton flavor mixing matrix (PMNS matrix) and the
quark flavor mixing matrix (CKM matrix) may be connected implicitly through a
relation between the neutrino Dirac Yukawa coupling $Y_D$ and the quark Yukawa
couplings. In this paper, we study whether $Y_D$ can satisfy, in the flavor
basis where the charged lepton Yukawa and right-handed neutrino Majorana mass
matrices are diagonal, the relation $Y_D \propto {\rm
diag}(y_d,y_s,y_b)V_{CKM}^T$ or $Y_D \propto {\rm diag}(y_u,y_c,y_t)V_{CKM}^*$
without contradicting the current experimental data on quarks and neutrino
oscillations. We search for sets of values of the neutrino Dirac CP phase
$\delta_{CP}$, Majorana phases $\alpha_2,\alpha_3$, and the lightest active
neutrino mass that satisfy either of the above relations, with the normal or
inverted hierarchy of neutrino mass. In performing the search, we consider
renormalization group evolutions of the quark masses and CKM matrix and the
propagation of their experimental errors along the evolutions. We find that
only the former relation $Y_D \propto {\rm diag}(y_d,y_s,y_b)V_{CKM}^T$ with
the normal neutrino mass hierarchy holds, based on which we make a prediction
for $\delta_{CP},\,\alpha_2,\,\alpha_3$ and the lightest active neutrino mass.
