  We use the entanglement negativity, a bipartite measure of entanglement in
mixed quantum states, to study how multipartite entanglement constrains the
real-space structure of the ground state wavefunctions of $(2+1)$-dimensional
topological phases. We focus on the (Abelian) Laughlin and (non-Abelian)
Moore-Read states at filling fraction $\nu=1/m$. We show that a combination of
entanglement negativities, calculated with respect to specific cylinder and
torus geometries, determines a necessary condition for when a topological state
can be disentangled, i.e., factorized into a tensor product of states defined
on cylinder subregions. This condition, which requires the ground state to lie
in a definite topological sector, is sufficient for the Laughlin state. On the
other hand, we find that a general Moore-Read ground state cannot be
disentangled even when the disentangling condition holds.
