  The moir\'e system provides a tunable platform for exploring exotic phases of
materials. This article shows the possible realization of a non-Abelian state
characterized by the Moore-Read wavefunction in a half-filled moir\'e Chern
band, exemplified by twisted $\rm MoTe_2$. This is achieved by introducing
short-range repulsive three-body interaction. Exact diagonalization is employed
to examine the spectrum in finite size. The incompressibility of the system,
the degeneracy of the ground states, and the number of low-energy states
provide compelling evidence to identify the ground state as the Moore-Read
state. We further interpolate between the three-body interaction and Coulomb
interaction to show a phase transition between the composite Fermi-liquid and
the Moore-Read state. Finally, we consider the effect of band mixing and derive
the three-body interaction using perturbation theory. By exploring the
conditions under which band mixing effects mimic short-range repulsive
three-body interaction we provide insights towards realizing non-Abelian phases
of matter in the moir\'e system.
