  In this paper we consider a spin-$\frac{3}{2}$ dark matter (DM) particle
coupled to neutrinos as a viable candidate to produce the observed DM relic
density through the thermal freeze-out mechanism. The couplings of DM to
neutrinos is considered first in a most general dimension six effective field
theory framework. We then consider two specific neutrino-portal models
discussed in the literature. In the first model DM couples to the standard
model neutrinos through mixing generated by a sterile pseudo-Dirac massive
neutrino and the second model we consider is the widely studied $U(1)_{L_\mu -
L_\tau}$ gauge symmetric model. For each of these models we explore the
parameter space required to generate the observed relic density. The
constraints on the parameters of these models from the existing and proposed
neutrino experiments as well as from existing cosmological and astrophysical
bounds are considered in the context of the relic density calculations.
