The KLM + KLN Auger electron spectrum of Cu (Z = 29) emitted in the electron capture decay of radioactive 65Zn in a solid matrix was investigated for the first time using a combined electrostatic electron spectrometer adjusted to the 7 eV instrumental resolution. Energies and relative intensities of nine resolved spectrum components were determined and compared with theoretical expectations. An agreement within 3σ was found between the semi-empirical predictions for the KLM transition energies by Larkins and the experimental data with the exception of the weak (KL2M4,5 + KL2N1) and (KL3M4,5 + KL3N1) lines where the differences reached 5σ. From a comparison of the measured relative KLM transition intensities with available theoretical results a conclusion was derived that calculations of the KLM transition rates at Z = 29 should be based on intermediate coupling of angular momenta and take into account relativistic effects.