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We investigated the crystal growth, electron paramagnetic resonance (EPR) and optical absorption spectra of L-threonine doped with Cu2+. The quality, size and habit of the single crystals grown from aqueous solution by the slow solvent evaporation and by the cooling method vary when the impurities are introduced during the growth process. The angular variations of the EPR spectra of single crystal samples at room temperature and 9.77 GHz with the magnetic field orientation in three crystal planes (ab, bc and ac) show the presence of copper impurities in four symmetry related interstitial sites of the unit cell. These spectra display well resolved hyperfine couplings of the S = ½ of Cu2+ with the ICu=3/2 of the copper nuclei. Additional hyperfine splittings, well resolved only for specific orientations of the magnetic field, indicate that the copper ions have two N ligands with approximately equal hyperfine couplings. The principal values of the g and ACu tensors calculated from the EPR data are g1= 2.051(1), g2 = 2.062(2), g3 = 2.260(2), A1= 16.9(5)10-4 cm-1, A2= 21.8(6)10-4 cm-1, A3= 180.0(5)10-4 cm-1. The principal directions corresponding to g3 and to A3 are coincident within the experimental error and reflect the orientation of the bonding planes of the copper ions in the crystal. The values of the crystal field parameters are evaluated from the optical absorption spectrum and the bonding parameters of the Cu impurities in the crystal are calculated and analyzed. The EPR and optical absorption results are discussed in terms of the crystal structure of L-threonine and the electronic structure of the Cu2+ ions, and compared with data reported for other systems. The effect of the impurities in the growth and habit of the crystals is discussed.