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.
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