The introduction of C-13 atoms into two cyano groups in the mixed-valence molecular conductor (DMe-DCNQI)2Cu, where DMe-DCNQI is 2,5-dimethyl-N,N'-dicyanoquinonediimine, non-deuterated and selectively deuterated at the methyl groups, was carried out. Isotope purity for C-13 was higher than 98 atom%. The impurity content (Li, Na, K, Mg, Ti, Mn, Fe, Co, Ni, Zn, Si) was less than 0.002 wt.% (inductively coupled plasma mass spectrometry method). Electrical resistivity measurements have shown apparent and reproducible shifts of the temperatures for phase transitions in each C-13-containing salt. This unexpected isotope effect indicates that the electronic state of (DMe-DCNQI)2Cu is quite sensitive to perturbations in the coordination around Cu.