  A pseudo-Riemannian manifold is called CSI if all scalar polynomial
invariants constructed from the curvature tensor and its covariant derivatives
are constant. In the Lorentzian case, the CSI spacetimes have been studied
extensively due to their application to gravity theories. It is conjectured
that a CSI spacetime is either locally homogeneous or belongs to the subclass
of degenerate Kundt metrics. Independent of this conjecture, any CSI spacetime
can be related to a particular locally homogeneous degenerate Kundt metric
sharing the same scalar polynomial curvature invariants. In this paper we will
invariantly classify the entire subclass of locally homogeneous CSI Kundt
spacetimes which are of alignment type {\bf D} to all orders and show that any
other CSI Kundt metric can be constructed from them.
