  Transverse-field muon-spin rotation ($\mu$SR) experiments were performed on a
single crystal sample of the non-centrosymmetric system MnSi. The observed
angular dependence of the muon precession frequencies matches perfectly the one
of the Mn-dipolar fields acting on the muons stopping at a 4a position of the
crystallographic structure. The data provide a precise determination of the
magnetic dipolar tensor. In addition, we have calculated the shape of the field
distribution expected below the magnetic transition temperature $T_C$ at the 4a
muon-site when no external magnetic field is applied. We show that this field
distribution is consistent with the one reported by zero-field $\mu$SR studies.
Finally, we present ab initio calculations based on the density-functional
theory which confirm the position of the muon stopping site inferred from
transverse-field $\mu$SR. In view of the presented evidence we conclude that
the $\mu$SR response of MnSi can be perfectly and fully understood without
invoking a hypothetical magnetic polaron state.
