  If the conformal holonomy group $Hol(\mathcal{T})$ of a simply connected
space with conformal structure of signature $(2p-1,2q-1)$ is reduced to
$\U(p,q)$ then the conformal holonomy is already contained in the special
unitary group $\SU(p,q)$. We present two different proofs of this statement,
one using conformal tractor calculus and an alternative proof using Sparling's
characterisation of Fefferman metrics.
