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The rotational spectral lines of c-C$_3$H$_2$ and two kinds of the $^{13}$Cisotopic species, c-$^{13}$CCCH$_2$ ($C_{2v}$ symmetry) and c-CC$^{13}$CH$_2$($C_s$ symmetry) have been observed in the 1-3 mm band toward the low-massstar-forming region L1527. We have detected 7, 3, and 6 lines of c-C$_3$H$_2$,c-$^{13}$CCCH$_2$ , and c-CC$^{13}$CH$_2$, respectively, with the Nobeyama 45 mtelescope, and 34, 6, and 13 lines, respectively, with the IRAM 30 m telescope,where 7, 2, and 2 transitions, respectively, are observed with the bothtelescopes. With these data, we have evaluated the column densities of thenormal and $^{13}$C isotopic species. The [c-C$_3$H$_2$]/[c-$^{13}$CCCH$_2$]ratio is determined to be $310\pm80$, while the[c-C$_3$H$_2$]/[c-CC$^{13}$CH$_2$] ratio is determined to be $61\pm11$. The[c-C$_3$H$_2$]/[c-$^{13}$CCCH$_2$] and [c-C$_3$H$_2$]/[c-CC$^{13}$CH$_2$]ratios expected from the elemental $^{12}$C/$^{13}$C ratio are 60-70 and 30-35,respectively, where the latter takes into account the statistical factor of 2for the two equivalent carbon atoms in c-C$_3$H$_2$. Hence, this observationfurther confirms the dilution of the $^{13}$C species in carbon-chain moleculesand their related molecules, which are thought to originate from the dilutionof $^{13}$C$^+$ in the gas-phase C$^+$ due to the isotope exchange reaction:$\mathrm{^{13}C^++CO\rightarrow{}^{13}CO+C^+}$. Moreover, the abundances of thetwo $^{13}$C isotopic species are different from each other. The ratio ofc-$\mathrm{^{13}CCCH_2}$ species relative to c-$\mathrm{CC^{13}CH_2}$ isdetermined to be $0.20\pm0.05$. If $^{13}$C were randomly substituted for thethree carbon atoms, the [c-$\mathrm{^{13}CCCH_2}$]/[c-$\mathrm{CC^{13}CH_2}$]ratio would be 0.5. Hence, the observed ratio indicates thatc-$\mathrm{CC^{13}CH_2}$ exists more favorably. Possible origins of thedifferent abundances are discussed.

Abundance Anomaly of the $^{13}$C Isotopic Species of c-C$_3$H$_2$ in the Low-Mass Star Formation Region L1527