  We discuss the possible origin of non-zero reactor mixing angle $\theta_{13}$
and Dirac CP phase $\delta_{CP}$ in the leptonic sector from a combination of
type I and type II seesaw mechanisms. Type I seesaw contribution to neutrino
mass matrix is of tri-bimaximal (TBM) type which gives rise to vanishing
$\theta_{13}$ leaving the Dirac CP phase undetermined. If the Dirac neutrino
mass matrix is assumed to take the diagonal charged lepton type structure, such
a TBM type neutrino mass matrix originating from type I seesaw corresponds to
real values of Dirac Yukawa couplings in the terms $Y_{ij} \bar{L_i} H N_j$.
This makes the process of right handed heavy neutrino decay into a light
neutrino and Higgs $(N \rightarrow \nu H)$ CP preserving ruling out the
possibility of leptogenesis. Here we consider the type II seesaw term as the
common origin of non-zero $\theta_{13}$ and $\delta_{CP}$ by taking it as a
perturbation to the leading order TBM type neutrino mass matrix. First, we
numerically fit the type I seesaw term by taking oscillation as well as
cosmology data and then compute the predictions for neutrino parameters after
the type II seesaw term is introduced. We consider a minimal structure of the
type II seesaw term and check whether the predictions for neutrino parameters
lie in the $3\sigma$ range. We also compute the predictions for baryon
asymmetry of the Universe by considering type II seesaw term as the only source
of CP violation and compare it with the latest cosmology data.
