  Real-analytic CR functions on real-analytic CR singular submanifolds are not
in general restrictions of holomorphic functions, unlike in the CR nonsingular
case. We give a simple condition that completely characterizes those quadric CR
singular manifolds of codimension 2 in ${\mathbb C}^{n+1}$ for which an
extension result holds. Consequently, we obtain an extension result for general
real-analytic CR singular submanifolds of codimension 2. As applications we
give a condition for the flattening of such submanifolds, and we classify CR
singular images of CR submanifolds up to second order.
