  It is known that in contrast with the E-mode polarization, the B-mode
polarization of the Cosmic Microwave Background cannot be generated by the
Compton scattering in the case of scalar mode of metric perturbation. However
it is possible to generate the B-mode by the Compton scattering in the case of
tensor mode of metric perturbation. For this reason, the ratio of tensor to
scalar modes of metric perturbation ($r\sim C_{Bl}/C_{El}$) is estimated by
comparing the B-mode power spectrum with the E-mode at least for small $l$. We
study the CMB polarization specially B-mode due to the weak interaction of
Cosmic Neutrino Background (CNB) and CMB, in addition to the Compton scattering
in both cases of scalar and tensor metric perturbations. It is shown that the
power spectrum $C_{Bl}$ of the B-mode polarization receives some contributions
from scalar and tensor modes, which have effects on the value of $r$-parameter.
We also show that the B-mode polarization power spectrum can be used as an
indirect probe into the CNB.
