We present $81$ near-infrared (NIR) spectra of $30$ Type II supernovae (SNe II) from the Carnegie Supernova Project-II (CSP-II), the largest such dataset published to date. We identify a number of NIR features and characterize their evolution over time. The NIR spectroscopic properties of SNe II fall into two distinct groups. This classification is first based on the strength of the He I $lambda1.083,mu$m absorption during the plateau phase; SNe II are either significantly above (spectroscopically strong) or below $50$ angstroms (spectroscopically weak) in pseudo equivalent width. However between the two groups, other properties, such as the timing of CO formation and the presence of Sr II, are also observed. Most surprisingly, the distinct weak and strong NIR spectroscopic classes correspond to SNe II with slow and fast declining light curves, respectively. These two photometric groups match the modern nomenclature of SNe IIP and IIL. Including NIR spectra previously published, 18 out of 19 SNe II follow this slow declining-spectroscopically weak and fast declining-spectroscopically strong correspondence. This is in apparent contradiction to the recent findings in the optical that slow and fast decliners show a continuous distribution of properties. The weak SNe II show a high-velocity component of helium that may be caused by a thermal excitation from a reverse-shock created by the outer ejecta interacting with the red supergiant wind, but the origin of the observed dichotomy is not understood. Further studies are crucial in determining whether the apparent differences in the NIR are due to distinct physical processes or a gap in the current data set.
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