Ge73 and Co59 nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) measurements have been performed on a Ge73-enriched single-crystalline sample of the ferromagnetic superconductor UCoGe in the paramagnetic state. The Ge73 NQR parameters deduced from NQR and NMR are close to those of another isostructural ferromagnetic superconductor URhGe. The Knight shifts of the Ge and Co sites are well scaled to each other when the magnetic field is parallel to the b or c axis. The hyperfine coupling constants of Ge are estimated to be close to those of Co. The large difference of spin susceptibilities between the a and b axes could lead to the different response of the superconductivity and ferromagnetism with the field parallel to these directions. The temperature dependence of the nuclear spin-lattice relaxation rates 1/T1 at the two sites is similar to each other above 5 K. These results indicate that the itinerant U-5f electrons are responsible for the ferromagnetism in this compound, consistent with previous studies. The similarities and differences in the three ferromagnetic superconductors are discussed.