The holographic neutron star provides a strong coupling description for a highly degenerate metallic state on a sphere. Its phase space can be split into two different sectors, with an unstable region at intermediate degeneracies. We investigate the critical nature of such region, by analyzing the asymptotic behavior of a scalar probe to compute the two-point correlator of the boundary theory. We show that in the stable region the correlator is dominated by the normal modes, whereas it displays a critical power-law behavior as we move into the unstable region.