  Understanding whether the bulge or the halo provides the primary link to the
growth of supermassive black holes has strong implications for galaxy evolution
and supermassive black hole formation itself. In this paper, we approach this
issue by investigating extragalactic globular cluster (GC) systems, which can
be used to probe the physics of both the bulge and the halo of the host galaxy.
We study the relation between the supermassive black hole masses M_BH and the
globular cluster system velocity dispersions sigma_GC using an updated and
improved sample of 21 galaxies. We exploit the dichotomy of globular cluster
system colours, to test if the blue and red globular clusters correlate
differently with black hole mass. This may be expected if they trace the
potentially different formation history of the halo and of the bulge of the
host galaxy respectively. We find that M_BH correlates with the total GC system
velocity dispersion, although not as strongly as claimed by recent work of
Sadoun & Colin. We also examine the M_BH - sigma_GC relation for
barred/bar-less and core/non-core galaxies, finding no significant difference,
and for the first time we quantify the impact of radial gradients in the GC
system velocity dispersion profile on the M_BH - sigma_GC relation. We
additionally predict M_BH in 13 galaxies, including dwarf elliptical galaxies
and the cD galaxy NGC 3311. We conclude that our current results cannot
discriminate between the bulge/halo scenario. Although there is a hint that the
red GC velocity dispersion might correlate better with M_BH than the blue GC
velocity dispersion, the number statistics are still too low to be certain.
