We compare the observational and theoretical spectra of the $Delta v$ = 2 CO bands in a range of M dwarfs. We investigate the dependence of theoretical spectra on effective temperatures as well as carbon abundance. In general we find that the synthetic CO bands fit the observed data extremely well and are excellent diagnostics. In particular the synthetic spectra reasonably match observations and the best fit temperatures are similar to those found by empirical methods. We also examine the CDC isotopic ratio. We find that fundamental $^{13}$CO bands around 2.345 and 2.375 $mu$m are good discriminators for the CDC ratio in M dwarfs. The 2.375 $mu$m is more useful because it doesnt suffer such serious contamination by water vapour transitions. Our current dataset does not quite have the wavelength coverage to perform a reliable determination of the CDC ratio in M dwarfs. For this we recommend observing the region 2.31--2.40 $mu$m at a resolution of better than 1000. Alternatively the observational problems of contamination by water vapour at 2.345 $mu$m maybe solved by observing at resolutions of around 50000. We also investigated the possibility of using the $Delta v$ = 1 CO bands around 4.5 $mu$m. We find that the contamination due to water vapour is even more of a problem at these wavelengths.
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