  Involutivity is a well known necessary condition for integrability of smooth
tangent distributions. We show that this condition is still necessary for
integrability with Sobolev surfaces. We specialize our study to the left
invariant horizontal distribution of the first Heisenberg group $\H^1$. Here we
answer a question raised in a paper by Z.M.Balogh, R.Hoefer-Isenegger,
J.T.Tyson.
