Bulk n-type ${\mathrm{Cd}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$Te crystals heavily doped with Ga are known to exhibit strong persistent photoconductivity (PPC) at low temperatures (below \ensuremath{\sim}100 K). In order to identify the origin of the PPC effect, we investigated the electronic properties of deep-level defects present in this material by deep-level transient spectroscopy (DLTS) and by thermally stimulated capacitance (TSCAP) measurements. We used a ${\mathrm{Cd}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$Te crystal with x=0.03 and a Ga doping level of 1\ifmmode\times\else\texttimes\fi{}${10}^{19}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$. The DLTS measurements revealed the presence of two deep levels, with thermal activation energies for electron emission of 0.25 and 0.43 eV. The electron capture process to the 0.25-eV level was found to be thermally activated, with a thermal energy barrier of 0.11 eV. DLTS measurements performed after sub-band-gap illumination at low temperatures established that, in addition to the PPC effect, the illumination causes also a strong increase in the concentration of the 0.25-eV states, which persist to temperatures as high as T=200 K. This finding indicates that---in addition to the metastability of conduction electrons with respect to the 0.25-eV states, which results in the PPC below 100 K---the 0.25-eV states are also metastable with respect to other (ground) states from which they are created by photoexcitation. Our TSCAP measurements detected also two transitions to two different deep levels, in agreement with these results. The first of these levels is donorlike, with an activation energy of 0.21 eV. The second level is acceptorlike, and the electron transition to this level requires a thermal energy of several hundreds of meV. Because the concentrations of both the 0.25- and the 0.43-eV states found by DLTS appear to be very close to each other, we propose a single defect model with two charge states, attributing the 0.43-eV level to an acceptorlike two-electron ground state of the defect, and the 0.25-eV level to the excited, donorlike one-electron state. According to this model, the defect possesses a positive Hubbard correlation energy (positive-U system). We discuss a configuration coordinate diagram of the defect in the paper.