The rotational spectra of three C-13 isotopic species of the linear C3H radical in the (2) Pi(r) ground vibronic state and the (2) Sigma(mu) vibronic state of the nu(4) (HCC bending) vibrational mode were observed by using a source-modulated spectrometer. The radical was produced in a free-space cell by a glow discharge in a mixture of C2H2, He, and (CO)-C-13. The rotational, spin-rotation interaction, Lambda-type doubling, and hyperfine interaction constants were determined from the analysis of the observed spectra, where vibronic interaction between the (2) Pi, and (2) Sigma(mu) states was taken into account. The r(s) structure of C3H, denoted by CalphaCbetaCgammaH, was derived from the rotational constants for the normal, deuterated, and three C-13 species : r(s)(C-alpha-C-beta)=1.3263(1) Angstrom, r(s)(C-beta-C-gamma)=1.2539(2) Angstrom, and r(s)(C-gamma-H)=1.0171(1) Angstrom. The short C-H distance is interpreted in terms of a large amplitude motion of the nu(4) mode, whose vibrational energy is very low due to the Renner-Teller effect. An ab initio molecular orbital calculation was carried out, and the structure in which the HCC angle is bent was found to be slightly more stable than the linear structure. The spin densities of three carbon atoms are derived from the hyperfine interaction constants, and they are discussed in connection to the quasilinear nature of the molecule.