  In a previous paper, one of us calculated iron K$\alpha$ line profiles
emitted from possible accretion disks around traversable wormholes as a first
step to use X-ray reflection spectroscopy to search for astrophysical wormholes
in active galactic nuclei. In the present paper, we extend that work and
construct an XSPEC model for the whole relativistic reflection spectrum. We
apply our model to XMM-Newton and NuSTAR observations of the supermassive
object in MCG-6-30-15 and we check whether these observations prefer the
hypothesis that the central body is a Kerr black hole or a traversable
wormhole. We find that the two models provide equally good fits, so with the
available data we cannot distinguish the black hole and wormhole scenarios.
