Although rapid eye movement (REM) sleep is conventionally treated as a unified state, it comprises two distinct microstates: phasic and tonic REM. Recent research emphasizes the importance of understanding the interplay between these microstates, hypothesizing their role in transient shifts between sensory detachment and external awareness. Previous studies primarily employed linear metrics to probe cognitive states, such as oscillatory power, while in this study, we adopt Lempel-Ziv Complexity (LZC), to examine the nonlinear features of electroencephalographic (EEG) data from the REM microstates and to gain complementary insights into neural dynamics during REM sleep. Our findings demonstrate a noteworthy reduction in LZC during phasic REM compared to tonic REM states, signifying diminished EEG complexity in the former. Additionally, we noted a negative correlation between decreased LZC and delta band power, along with a positive correlation with alpha band power. This study highlights the potential of nonlinear EEG metrics, particularly LZC, in elucidating the distinct features of REM microstates. Overall, this research contributes to advancing our understanding of the complex dynamics within REM sleep and opens new avenues for exploring its implications in both clinical and nonclinical contexts.