The germanium methylidyne (GeCH) radical has been studied at high resolution by laser-induced fluorescence spectroscopy in a skimmed molecular beam. The radical was produced in a pulsed discharge jet source using methyltrichlorogermane as the precursor. Single rotational lines of the (A) over tilde (2)Sigma (+)-(X) over tilde (2)Pi (3/2) component of the 0(0)(0) band at 14 070 cm(-1) were recorded with linewidths of 35 MHz, showing resolved proton magnetic hyperfine splittings. The observed hyperfine splittings of 12 rotational lines were satisfactorily modeled by varying a single upper state Fermi contact parameter, giving b(F) = 163(2) MHz. Optical Stark measurements were performed on the (GeCH)-Ge-74 P-11(3/2)F' = 1 hyperfine transition and the permanent electric dipole moments determined to be mu((X) over tilde (2)Pi) = 0.122(2) D and mu((A) over tilde (2)Sigma (+)) = 1.29(2) D. Our ab initio predictions of the dipole moments and excited state Fermi contact parameter are in fair agreement with experiment. The magnitudes of the determined parameters are discussed based on the molecular orbitals and compared to similar measurements on SiCH.