  Cosmological data have provided new constraints on the number of neutrino
species and the neutrino mass. However these constraints depend on assumptions
related to the underlying cosmology. Since a correlation is expected between
the number of effective neutrinos N_{eff}, the neutrino mass \sum m_\nu, and
the curvature of the universe \Omega_k, it is useful to investigate the current
constraints in the framework of a non-flat universe. In this paper we update
the constraints on neutrino parameters by making use of the latest cosmic
microwave background (CMB) data from the ACT and SPT experiments and consider
the possibility of a universe with non-zero curvature. We first place new
constraints on N_{eff} and \Omega_k, with N_{eff} = 4.03 +/- 0.45 and 10^3
\Omega_k = -4.46 +/- 5.24. Thus, even when \Omega_k is allowed to vary, N_{eff}
= 3 is still disfavored with 95% confidence. We then investigate the
correlation between neutrino mass and curvature that shifts the 95% upper limit
of \sum m_\nu < 0.45 eV to \sum m_\nu < 0.95 eV. Thus, the impact of assuming
flatness in neutrino cosmology is significant and an essential consideration
with future experiments.
