  In this paper we determine all the simply connected non-degenerate CR Lie
groups, which are flat with respect to the Cartan connection: in terms of
associated Lie algebras, we assert that the only Cartan flat non-degenerate CR
Lie algebras are $\mathfrak{su}(2)$, $\mathfrak{sl}(2,\mathbb{R})$,
$\mathfrak{aff}(\mathbb{R}) \oplus \mathbb{R}$, and $\mathfrak{h}_{2m+1}$ with
its modifications, where $\mathfrak{aff}(\mathbb{R})$ is the affine Lie algebra
of dimension 2 and $\mathfrak{h}_{2m+1}$ is the Heisenberg Lie algebra of
dimension $2m+1$. Furthermore, we determine all the (flat and non-flat)
non-degenerate CR structures on each of these Lie groups.
