Carbon ion radiotherapy is an attractive alternative to conventional radiotherapy, especially in case of deep-seated and radio-resistant tumors. As a consequence of inelastic nuclear reactions between primary particles and patient's tissues, the primary carbon ions may undergo nuclear fragmentation. The resulting decrease of primary ions and production of secondary fragments have to be carefully considered for accurate dose calculations in the treatment planning systems. The experimental data currently available provide only general information on carbon ion fragmentation and are not sufficient to cover the entire range of beam energies, target configurations and compositions relevant for radiotherapy. Therefore, new investigations were carried out to analyse the outcomes of the inelastic nuclear reaction processes on a single-ion-based approach. Measurements were performed at HIT, using 430 MeV/u carbon ion beams crossing water and PMMA targets. Unique in this method is the possibility of measuring number and type of fragments produced from each single carbon ion, provided that they are within the acceptance of the experimental apparatus. Concerning the amount of residual carbon ions behind water and PMMA targets with the same water equivalent thickness (WET), no significant differences were found. The experimental attenuation curve was well reproduced by the simulations. However, in the experiments, differences were observed regarding the amount of secondary fragments produced in water and in PMMA targets with the same WET. Differences were also found between experiments and simulations. These findings should be considered when dosimetric measurements are performed with PMMA instead of water phantoms. The found differences between experiments and simulations may contribute to improve the nuclear interaction and fragmentation models in Monte Carlo codes.