Quantitative determination of atmospheric CO2 concentration by remote sensing relies on accurate line parameters. Lamb dips of the lines up to J'' = 72 in the 30013-00001 band at 1605 nm were measured using a comb-locked cavity ring-down spectrometer, and the positions were determined with an accuracy of a few kHz. A simple effective Hamiltonian model can fit the rotational energies in the 30013 state ideally within the experimental accuracy, indicating that the vibrational state is well-isolated and can be regarded as free from perturbations. From a comparison between other bands using a similar analysis, we conclude that the transitions in the 30013-00001 band could be more suitable as reference lines for sensing applications with the potentially improved line parameter accuracy.