The local density approximation is used to study the ground state superfluid properties of harmonically trapped p-wave Fermi gases as a function of fermion-fermion attraction strength. While the density distribution is bimodal on the weakly attracting BCS side, it becomes unimodal with increasing attraction and saturates towards the BEC side. This non-monotonic evolution is related to the topological gapless to gapped phase transition, and may be observed via radio-frequency spectroscopy since quasi-particle transfer current requires a finite threshold only on the BEC side.
