We report calculated H-2 nuclear quadrupole coupling constants and asymmetry parameter in deuterated crystalline oxalic acid dihydrated polymorphs within a full-potential linear combination of Gaussian-type orbitals employing both Density Functional Theory and Hartree-Fock approximation. The Becke's hybrid exchange B3 and the Lee, Yang and Parr correlation functionals were employed. Their dependence with basis set, interelectronic correlation, structural changes and crystal field environment are reported.