This assembly of a trim part of thermoplastic material for a motor vehicle with another part having a thin portion of thermoplastic material is such that the thin portion presents through orifices and the melting of the trim part together with the thin portion is localized solely at the outlines of the through orifices. In the assembly method, the melting of material is obtained by welding, by means of tangential vibrations of a bit in an ultrasound frequency range. The tangential vibrations are applied to the thin portion of the other part so as to form at least one through orifice in said part and so as to cause melting of said part together with the trim part at the outline of the orifice.