Electron correlation effects to the four coupling mechanisms which contribute to the isotropic nuclear spin-spin coupling constant, the Fermi contact (FC), paramagnetic spin-orbit (PSO), spin-dipole (SD), and diamagnetic spin-orbit (DSO) are studied using the equation of motion coupled-cluster (EOM-CC) method. The second-order properties are expressed as a sum-over state (SOS) using EOM-CC intermediate state wave functions. This formulation is simple, accurate, computationally convenient, and involves no truncation. Several molecules, HF, CO, N-2, H2O, NH3, and HCl which have been previously shown to have large noncontact contributions are investigated using the EOM-CC method and the results are compared with experiment and other theoretical methods, including polarization propagator and finite-field MBPT(2) methods. Using fairly large basis sets, the EOM-CCSD provides results which agree with experimental indirect nuclear spin-spin coupling constants to within an average error of 13%.