  In the quark sector, Jarlskog rephasing invariant $\rm{J_{CP}}$ has important
implications for the CP violation as well as phase structure of the quark mass
matrices. In fact all CP violating effects in this sector are proportional to
the magnitude of the imaginary part of $\rm{J_{CP}}$.
  With the observation of non-zero and relatively large reactor mixing angle
$\theta_{13}$, it is widely believed that CP might be violated in the lepton
sector. The recent global best fits of neutrino oscillation indicates the
preference of CP violation over CP conservation at relatively large confidence
level. These experimental observations warrant to re-investigate the CP-odd
weak basis invariants at low energies, and also explore their implications for
CP violation in the context of texture two zero neutrino mass matrix.
