The molecular torus in AGN is a key element in the unified scheme of AGN. We here present an overview of our attempts to reveal the structures and physical conditions of molecular tori using the near-infrared (4.6 micron) ro-vibrational transitions of CO. Our strategy is to observe the molecular tori in CO absorption with the dust emission from the sublimation layer around AGN as background sources. Many transitions at difference energy levels (v = 0-1, delta J = +1 or -1) are expected to enable reliable measurements of the temperatures and the column densities of molecules in the tori.  Our observations consist of two parts: one is those with AKARI and the other is those with Subaru. AKARI observation covers various targets, although the spectral resolution is rather limited. Baba et al. (2018) showed that many obscured AGN showed CO features in absorption, but not all the Seyfert 2 galaxies. This indicates that the central region of AGN could have more complicated structures than the unified scheme suggests. On the basis of Subaru observations, Shirahata et al. (2013) attributed the high temperature and large column densities observed in CO absorption features to the warm molecular components excited by the X-ray radiation from the center. Onishi et al. (in preparation) decomposes the absorption features into several components and proposes a model of torus structures to explain the observations. Our result indicate that the absorption observations are a can reveal critical AGN-torus features, which cannot be shown by emission observations.