  $^{73}$Ge and $^{59}$Co nuclear magnetic resonance (NMR) and nuclear
quadrupole resonance (NQR) measurements have been performed on a
$^{73}$Ge-enriched single-crystalline sample of the ferromagnetic
superconductor UCoGe in the paramagnetic state. The $^{73}$Ge 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 $1/T_1$ 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.
