  We study compact Sasakian manifolds whose Tondeur connection has holonomy
group either trivial or contained in Sp(n). We show that the first condition
forces the manifold to be a compact quotient of the Heisenberg Lie group, while
in the simply-connected case a Sasakian structure has the holonomy of the
Tondeur connection contained in Sp(n) if and only if there exists a transverse
hypercomplex structure. This latter result is the "Sasakian version" of a
theorem of Verbitsky.
