  A tensor invariant is defined on a paraquaternionic contact manifold in terms
of the curvature and torsion of the canonical paraquaternionic connection
involving derivatives up to third order of the contact form. This tensor,
called paraquaternionic contact conformal curvature, is similar to the Weyl
conformal curvature in Riemannian geometry, the Chern-Moser tensor in CR
geometry, the para contact curvature in para CR geometry and to the
quaternionic contact conformal curvature in quaternionic contact geometry.
  It is shown that a paraquaternionic contact manifold is locally
paraquaternionic contact conformal to the standard flat paraquaternionic
contact structure on the paraquaternionic Heisenberg group, or equivalently, to
the standard para 3-Sasakian structure on the paraquaternionic pseudo-sphere
iff the paraquaternionic contact conformal curvature vanishes.
