  In this paper, we put constraints on neutrino properties such as mass
  $m_{\nu}$ and degeneracy parameters $\xi_i$ from WMAP5 data and light element
abundances by using a Markov chain Monte Carlo (MCMC) approach. In order to
take consistently into account the effects of the degeneracy parameters, we run
the Big Bang Nucleosynthesis code for each value of $\xi_i$ and the other
cosmological parameters to estimate the Helium abundance, which is then used to
calculate CMB anisotropy spectra instead of treating it as a free parameter. We
find that the constraint on $m_{\nu}$ is fairly robust and does not vary very
much even if the lepton asymmetry is allowed, and is given by $\sum m_\nu < 1.3
\rm eV$ ($95 % \rm C.L.$).
