The paper is devoted to the detailed study of electric and magnetic properties and magnetoelectric interactions in NH2(CH3)2Ga(SO4)2 × 6H2O crystals doped with chromium—DMAGaS:Cr. The temperature dependence of the specific heat revealed clear evidence of a series of phase transitions related to the electric dipoles ordering. The different types of the DMA cation ordering in the structure of DMAGaS:Cr were evidenced in the temperature evolution of the EPR spectra. In addition, a considerable magnetoelectric coupling was demonstrated within the paramagnetic and ferroelectric phase of DMAGaS:Cr crystal. In the narrow temperature range in the vicinity of the Curie point, this crystal was found to possess the largest values of the coefficient of ME interaction as well as the largest magnetodielectric effect within the family of ferroics with organic cation. The model describing the ME effect was proposed. The magnetic field through the magnetostriction effect changes the level of the local lattice deformations caused by metal ion substitution. The applied magnetic field changes Cr-Cr distances and modifies the hydrogen bonds and process of DMA group ordering, affecting spontaneous polarization.