In his paper "More is Different", Philip Warren Anderson claims to be in posession of a proof by which any stationary state of an Ammonia molecule (or anything really, again according to him, as the argument is based solely on the symmetry of space and time) has no electric dipole moment.
However, I have not been able to come by such a proof or think of one myself. As far as I know, stationary states (and ground states at that, in case he may have actually meant only those) do not in general share all symmetries of the Hamiltonian. With that taken into consideration, I cannot see why the dipole moment must vanish for such states, as they need not to have for example an inversion or rotational symmetry which would trivially lead to the required conclusion.
In his paper he mentions having learned of this alleged fact in a course on nuclear physics, if that helps by some chance with the obtaining of a proof.
