  We have carried out a careful magnetic neutron scattering study of the heavy
fermion compound \URuSi\ to probe the possible existence of a small magnetic
moment parallel to tetragonal basal plane in the "hidden-order" phase. This
small in-plane component of the magnetic moment on the uranium sites
$S_\parallel$ has been postulated by two recent models (rank-5
superspin/hastatic order) aiming to explain the hidden-order phase, in addition
to the well-known out-of-plane component $S_\perp ~ \approx~0.01-0.04
$\mu_B$/U. In order to separate $S_\parallel$ and $S_\perp$ we take advantage
of the condition that for magnetic neutron scattering only the components of
the magnetic structure that are perpendicular to the scattering vector $Q$
contribute to the magnetic scattering. We find no evidence for an in-plane
magnetic moment $S_\parallel$. Based on the statistics of our measurement, we
establish that the upper experimental limit for the size of any possible
in-plane component is $S^{\rm{max}}_\parallel ~ \leq~1\cdot 10^{-3} ~\mu_B$/U.
