A CR-structure on a 2n +1-manifold gives a conformal class of Lorentz metrics on the Fefferman S¹-bundle. This analogy is carried out to the quarternionic conformal 3-CR structure (a generalization of quaternionic CR- structure) on a 4n + 3 -manifold M. This structure produces a conformal class [g] of a pseudo-Riemannian metric g of type (4n + 3,3) on M × S³. Let (PSp(n +1,1), S4ⁿ⁺³) be the geometric model obtained from the projective boundary of the complete simply connected quaternionic hyperbolic manifold. We shall prove that M is locally modeled on (PSp(n +1,1), S4ⁿ⁺³) if and only if (M × S³ ,[g]) is conformally flat (i.e. the Weyl conformal curvature tensor vanishes).