  For a smooth strictly pseudoconvex hypersurface in a complex manifold, we
give a necessary and sufficient condition for being CR-diffeomorphic to a
real-analytic CR manifold. Our condition amounts to a holomorphic extension
property for the canonically associated function expressing $2$-jets of the
formal Segre varieties in terms of their $1$-jets. We also express this
condition in equivalent terms for a Fefferman type determinant
