The optical properties of paramagnetic CrN over the wavelength range $250\text{nm}–30\mu \text{m}$ were determined from transmission and reflection spectra of $44–11000\text{-nm}$-thick epitaxial CrN(001) layers that were grown on MgO(001) by ultrahigh vacuum magnetron sputtering at $700°\text{C}$ and were found to be pure cubic single crystals by x-ray diffraction $\omega \text{−}2\theta$, $\omega$, and $\phi$ scan analyses. The imaginary part of the dielectric function exhibits a steep onset at $\hslash \omega =0.64\text{eV}$ as well as peaks at $\hslash \omega =1.5$ and 2.9 eV due to direct interband transitions and indicates a depletion in the density of states at the Fermi level with an upper limit for free carriers of $3\times {10}^{19}{\text{cm}}^{-3}$. This is attributed to local magnetic moments that cause splitting of the $t_{2g}$ bands and the formation of an indirect band gap of $0.19\pm 0.46\text{eV}$, as estimated by comparing the optical transition energies with reported direct gap energies from calculations with different magnetic ordering and Coulomb interaction terms. The dielectric function shows a strong resonance at $\hslash {\omega }_0=48.7\pm 0.2\text{meV}$, and values of ${\epsilon }_{\text{dc}}=53\pm 5$ and ${\epsilon }_{\infty }=22\pm 2$ below and above the resonance, respectively, providing values for transverse and longitudinal optical phonon frequencies at the zone center of 11.7 THz and 18.2 THz (corresponding to $\hslash \omega =48.7\pm 0.2$ and $75.6\pm 6.8\text{meV}$), respectively, and a Born effective charge of $4.4\pm 0.9$. The vibrational frequencies are confirmed by Raman spectroscopy peaks at 800, 1170, and $1330{\text{cm}}^{-1}$ which are attributed to 2TO(X), 2LO(X), and 2LO(L) modes and correspond to single-phonon energies of 49.6 meV, 72.5 meV, and 82.5 meV, respectively. They are quantitatively comparable to those reported for ScN, a semiconductor with the same crystal structure as cubic CrN. In conclusion, both electronic interband transitions and optical phonon frequencies suggest that CrN is a Mott-Hubbard-type insulator with a small to negligible indirect band gap.