Our recent research on Th-bearing intermetallics revealed bulk superconductivity in ThPtSi. The critical temperature determined from the resistivity and magnetization data is Tc = 3.3 K. The compound crystallizes with the LaPtSi-type crystal structure (s.g. I41md) that lacks an inversion symmetry. The results of bulk properties measurements, e.g. nearly linear temperature dependence of the upper critical field, hint at unconventional superconductivity. The aim of this proposal is to verify the nature of the superconducting state in ThPtSi by means of detailed muon-SR study