The methyl CH-stretching overtone spectra of gaseous monohydrogenated nitromethane NO2CHD2 have been recorded with conventional near infrared spectroscopy in the Delta upsilon (CH)=1 to 4 regions and by intracavity laser photoacoustic spectroscopy in the Delta upsilon(CH)=5 and 6 regions. They all exhibit a complex structure with, at Delta upsilon(CH)=1 and 2, a characteristic asymmetric top vibration-rotation profile which vanishes as vibrational energy increases. These spectra have been analyzed with a theoretical model which takes into account in the adiabatic approximation the coupling between the anharmonic CH stretch described by a Morse potential and the quasifree internal rotation of the methyl group. All the parameters of this model (the zero point energy, the CH stretch frequency, the expansion coefficients of the dipole moment function) and their variation with the internal rotation coordinate have been determined from HF/6-31G** ab initio calculations, This simple calculation, which contains no adjustable parameters, successfully describes the relative intensity and frequency of each peak within a given overtone and accounts for the variation of the dipole moment function as the vibrational energy increases. Owing to the relative localization of the wave functions within the effective potential wells, the spectral features can be assigned to particular pseudoconformers. The outer bands correspond to rovibrational transitions associated with the parallel and perpendicular conformation of the CH bond versus the molecular plane, the central band is generated by "free rotor" rovibrational transitions. Fermi resonance phenomena lead to no sizeable IVR until the fifth overtone. The CH/CD interbond coupling shifts the overtone spectra toward high frequency and is responsible for some additional weaker features in the high overtone spectra(Delta upsilon=5 and 6).