Various neural health estimates have been shown to indicate the density of spiral ganglion neurons in animal and modeling studies of cochlear implants (CIs). However, when applied to human CI users, these neural health estimates based on psychophysical and electrophysiological measures are not consistently correlated with each other or with the speech recognition performance. This study investigated whether the neural health estimates have stronger correlations with the temporal and place pitch sensitivity than with the speech recognition performance. On five electrodes in 12 tested ears of eight adult CI users, polarity effect (PE), multipulse integration (MPI), and interphase gap (IPG) effect on the amplitude growth function (AGF) of electrically evoked compound action potential (ECAP) were measured to estimate neural health, while thresholds of amplitude modulation frequency ranking (AMFR) and virtual channel ranking (VCR) were measured to indicate temporal and place pitch sensitivity. AzBio sentence recognition in noise was measured using the clinical CI processor for each ear. The results showed significantly poorer AMFR and VCR thresholds on the basal electrodes than on the apical and middle electrodes. Across ears and electrodes, only the IPG offset effect on ECAP AGF had a nearly significant negative correlation with the VCR threshold after removing the outliers. No significant across-ear correlations were found between the mean neural health estimates, mean pitch-ranking thresholds, and AzBio sentence recognition score. This study suggests that the central axon demyelination reflected by the IPG offset effect may be important for the place pitch sensitivity of CI users and that the IPG offset effect may be used to predict the perceptual resolution of virtual channels for CI programming.