Absolute pitch (AP) is the ability to identify the pitch names of arbitrary musical tones without being given a reference pitch. The acquisition of AP typically requires early musical training, the critical time window for which is similar to that for the acquisition of a first language. This study investigated the left-right asymmetry of the auditory cortical functions responsible for AP by focusing on the T-complex of auditory evoked potentials (AEPs), which shows morphological changes during the critical period for language acquisition. AEPs evoked by a pure-tone stimulus were recorded in high-AP musicians, low-AP musicians, and non-musicians (n = 19 each). A balanced non-cephalic electrode (BNE) reference was used to examine the left-right asymmetry of the N1a and N1c components of the T-complex. As a result, a left-dominant N1c was observed only in the high-AP musician group, indicating "AP negativity," which has previously been described as an electrophysiological marker of AP. Notably, this hemispheric asymmetry was due to a diminution of the right N1c rather than enhancement of the left N1c. A left-dominant N1a was found in both musician groups, irrespective of AP. N1c and N1a exhibited no left-right asymmetry in non-musicians. Hence, music training and the acquisition of AP are both accompanied by a left-dominant hemispheric specialization of auditory cortical functions, as indexed by N1a and N1c, respectively, but the N1c asymmetry in AP possessors was due to reduced neural activities in the right hemisphere. The use of a BNE is recommended for evaluating these radially oriented components of the T-complex.