  We classify the germs of $\mathcal{C}^\infty$ CR manifolds that admit a
smooth CR contraction. We show that such a CR manifold is embedded into $\CC^n$
as a real hypersurface defined by a polynomial defining function consisting of
monomials whose degrees are completely determined by the extended resonances of
the contraction. Furthermore the contraction map extends to a holomorphic
contraction that coincides in fact with its polynomial normal form.
Consequently, several results concerning Complex and CR geometry are derived.
