The CH-stretching overtone spectra of the methyl group in gaseous nitromethane NO2CH2D have been recorded with conventional Fourier transform near-infrared spectroscopy in the Delta upsilon(CH) = 1 - 4 regions and by intracavity laser photoacoustic spectroscopy in the Delta upsilon(CH) = 5 and 6 regions. All spectra exhibit a complex structure; they have been analyzed with a theoretical model which takes into account, within the adiabatic approximation, the coupling of the anharmonic CH stretch vibrations, described by Morse potentials, with the quasifree internal rotation of the methyl group and with isoenergetic combination states involving methyl bending modes. Most of the parameters of this model, and their variation with the internal rotation coordinate (theta), are identical to ones used to account for the overtone spectra of the monohydrogenated and perhydrogenated species. Fermi resonance phenomena, also modeled with theta dependent parameters, lead to only weak intramolecular vibrational energy redistribution. This simple calculation successfully describes the relative intensity and frequency of each peak within a given overtone. The vibrational energy is seen to be localized at lower energy in the dihydrogenated compound [at the second overtone (upsilon = 3)] than in the perhydrogenated one [at the third overtone (v = 4)]. The overtone vibrations obtained from the calculations can be considered as normal modes up to Delta upsilon = 2 and as local modes from Delta upsilon = 3 to 6. However, at Delta upsilon = 3, the existence of a transitional regime, where normal and local modes coexist, can be demonstrated. The CH/CD interbond coupling shifts the overtone spectra toward high for some additional weaker features in the high overtone spectra (Delta upsilon = 5 and 6).