Electron paramagnetic resonance measurements of a new copper dithiocarbamate complex having liquid crystal properties are presented. Spectra have been measured using a frozen toluene solution at liquid nitrogen temperature as well as concentrated samples at different temperatures covering the solid and smectic phases range. The existence of a long range intermolecular exchange interaction at all the temperatures is established by the collapse of the hyperfine structure in the spectra of the condensed samples. The comparison of the principal effective g- values in the solid phase with those of the isolated molecule obtained from the toluene solution spectra indicates that in the solid, the molecules pack keeping their molecular axes parallel. The drastic changes observed in the spectra when the sample reaches the smectic phase are interpreted as a consequence of the structure of this mesophase and on the basis of the calamitic shape of the molecules. This led us to obtain the temperature dependence of the Saupe order parameter in the smectic phase from the thermal evolution of the spectra directly, without using any foreign probe. This also contrasts with the behaviour observed in others copper metallomesogens derived from Schiffs bases whose molecules depart significantly from cylindrical shape.