Single crystals of Ti${\mathrm{O}}_{2}$:${\mathrm{Cu}}^{2+}$ have been investigated at 20 K using the technique of electron paramagnetic resonance. The major features of the EPR spectra can be attributed to divalent copper ($3{d}^{9}$) in substitutional (${\mathrm{Ti}}^{4+}$) sites. Information has been gained about both isotopes of copper and about the interactions which concern this ion. For the substitutional site, the spin-Hamiltonian parameters in the $S=\frac{1}{2}$, $I=\frac{3}{2}$ manifold are: ${g}_{x}=2.109$, ${g}_{y}=2.094$, ${g}_{z}=2.346$, $A_{x}^{}{}_{}{}^{63}=+18.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ ${\mathrm{cm}}^{\ensuremath{-}1}$, $A_{y}^{}{}_{}{}^{63}=+27.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ ${\mathrm{cm}}^{\ensuremath{-}1}$, $A_{z}^{}{}_{}{}^{63}=\ensuremath{-}87.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ ${\mathrm{cm}}^{\ensuremath{-}1}$, $A_{x}^{}{}_{}{}^{65}=+18.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ ${\mathrm{cm}}^{\ensuremath{-}1}$, $A_{y}^{}{}_{}{}^{65}=+28.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ ${\mathrm{cm}}^{\ensuremath{-}1}$, $A_{z}^{}{}_{}{}^{65}=\ensuremath{-}93.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ ${\mathrm{cm}}^{\ensuremath{-}1}$, ${P}_{x}=\ensuremath{-}2.56\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, ${P}_{y}=\ensuremath{-}2.37\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, and ${P}_{z}=+4.93\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ ${\mathrm{cm}}^{\ensuremath{-}1}$. The magnitudes and relative signs of these parameters have been determined experimentally, while the absolute signs have been predicted theoretically from a model which gives a consistent picture of the ordering of the ${d}^{9}$ electronic states. In addition, the theoretical treatment gives a satisfactory estimate of $P$. Departure from tetragonality was taken into account. The covalency parameter ${\ensuremath{\alpha}}^{2}$ which measures the fraction of the hole wave function on the ${\mathrm{Cu}}^{2+}$ ion is found to be 0.71, and the factor $\ensuremath{\kappa}$ giving rise to isotropic hyperfine structure is found to be 0.31.