In order to detect ³He produced by the cold nuclear fusion, we measured ³He in Ti electrode in an electrolytic cell containing deuterium. All the ³He amounts in the electrode were more or less in the same order of magnitude as that of hot blanks in the measurement by mass spectrometry. There was no difference in ³He amounts between the run products using H₂O+LiH and D₂O+LiD as electrolyte, and no correlation with the experimental time of electrolysis. The result indicates that the fusion rate of deuterons was less than 3×10¹/sec, much lower than the value (4×10⁴) obtained by Fleischmann and Pons (1989). However, in our ³He measurement it was difficult to detect the fusion rate as low as 4×10^-1 given by Jones et al. (1989). The obtained upper limit of the fusion rate suggests that the electrolytic refining is not the cause of high ³He/⁴He ratios observed in metals.