Aims. Our main aim is to determine carbon-to-nitrogen and carbon isotope ratios for evolved giants in the open clusters NGC 2324, NGC 2477, and NGC 3960, which have turn-off masses of about 2 M⊙, and to compare them with predictions of theoretical models. Methods. High-resolution spectra were analysed using a differential synthetic spectrum method. Abundances of carbon were derived using the C2 Swan (0, 1) band heads at 5135 and 5635.5 Å. The wavelength interval 7940-8130 Å with strong CN features was analysed to determine nitrogen abundances and carbon isotope ratios. The oxygen abundances were determined from the [O I] line at 6300 Å. Results. The mean values of the CNO abundances are [C/Fe] = -0:35 ± 0:06 (s.d.), [N/Fe] = 0:28 ± 0:05, and [O/Fe] = -0:02 ± 0:10 in seven stars of NGC 2324; [C/Fe] = -0:26 ± 0:02, [N/Fe] = 0:39 ± 0:04, and [O/Fe] = -0:11 ± 0:06 in six stars of NGC 2477; and [C/Fe] = -0:39 ± 0:04, [N/Fe] = 0:32 ± 0:05, and [O/Fe] = -0:19 ± 0:06 in six stars of NGC 3960. The mean C/N ratio is equal to 0:92 ± 0:12, 0:91 ± 0:09, and 0:80 ± 0:13, respectively. The mean 12C/13C ratio is equal to 21 ± 1, 20 ± 1, and 16 ± 4, respectively. The 12C/13C and C/N ratios of stars in the investigated open clusters were compared with the ratios predicted by stellar evolution models. Conclusions. The mean values of the 12C/13C and C/N ratios in NGC 2324 and NGC 2477 agree well with the first dredge-up and thermohaline-induced extra-mixing models, which are similar for intermediate turn-off mass stars. The 12C/13C ratios in the investigated clump stars of NGC 3960 span from 10 to 20. The mean carbon isotope and C/N ratios in NGC 3960 are close to predictions of the model in which the thermohaline- and rotation-induced (if rotation velocity at the zero-age main sequence was 30% of the critical velocity) extra-mixing act together. [ABSTRACT FROM AUTHOR]