Aims. We have observed the N = 1−0 lines of CCH and its 13 C isotopic species toward a cold dark cloud, TMC-1 and a star-forming region, L1527, to investigate the 13 C abundances and formation pathways of CCH. Methods. The observations have been carried out with the IRAM 30 m telescope. Results. We have successfully detected the lines of 13 CCH and C 13 CH toward the both sources and found a significant intensity difference between the two 13 C isotopic species. The [C 13 CH]/[ 13 CCH] abundance ratios are 1.6 ± 0.4 (3σ) and 1.6 ± 0.1 (3σ) for TMC-1 and L1527, respectively. The abundance difference between C 13 CH and 13 CCH means that the two carbon atoms of CCH are not equivalent in the formation pathway. On the other hand, the [CCH]/[C 13 CH] and [CCH]/[ 13 CCH] ratios are evaluated to be larger than 170 and 250 toward TMC-1, and to be larger than 80 and 135 toward L1527, respectively. Therefore, both of the 13 C species are significantly diluted in comparison with the interstellar 12 C/ 13 C ratio of 60. The dilution is discussed in terms of a behavior of 13 C in molecular clouds.