  We derive a low energy effective field theory for chiral superfluids, which
accounts for both spontaneous symmetry breaking and fermionic ground-state
topology. Using the theory, we show that the odd (or Hall) viscosity tensor, at
small wave-vector, contains a dependence on the chiral central charge $c$ of
the boundary degrees of freedom, as well as additional non-universal
contributions. We identify related bulk observables which allow for a bulk
measurement of $c$. In Galilean invariant superfluids, only the particle
current and density responses to strain and electromagnetic fields are
required. To complement our results, the effective theory is benchmarked
against a perturbative computation within a canonical microscopic model.
