We show that biholomorphic automorphisms of a real analytic hypersurface in
Cn+1 can be considered as (pointwise) Lie symmetries of a holomorphic comp
letely overdetermined involutive second order PDE system defining its Segre
family. Using the classical S.Lie method we obtain a complete description
of infinitesimal symmetries of such a system and give a new proof of some w
ell known results of CR geometry.