Laser-induced fluorescence (LIF) measurements are made on the C2Σ+- X2II r (λ = 314 nm) transition of CD, which is produced by a microwave-excited Ar/CD4 process plasma. The experiment is realized by using a frequency-doubled cw ring dye laser as the tunable light source. Due to the small bandwidth (≈3 MHz) of the exciting UV laser, the exact line positions of spin-doubled rotational lines in the P-branch ( N” = 2 to 5 and N” = 8 to 13) of the first vibrational band ( v’ = v” = 0) could be determined. The resolution is limited only by Doppler broadening, which amounts in our plasma ( T = 450 K) to about 4 GHz. With these new values of line positions, a modified spin-splitting constant of γ = 0.051 ± 0.006 cm−1 is calculated.