We report in this paper an implementation of 4-component relativistic Hamiltonian based Equation-of-Motion Coupled-Cluster (EOMCC) theory for the calculation of ionization potential (IP), electron affinity (EA) and excitation energy (EE). In this work we utilize previously developed double group symmetry-based generalized tensor contraction scheme, and also extend it in order to carry out tensor contractions involving non-totally symmetric and odd-ranked tensors. Several approximated spin-free and two-component Hamiltonians can also be accessed in this implementation. We have applied this method to the halogen monoxide (XO, X= Cl, Br, I, At, Ts) species, in order to assess the quality of a few other recent EOMCC implementations, where spin-orbit coupling contribution has been approximated in different degree. Besides, we also have studied various excited states of CH₂IBr, CH₂I₂ and I₃^- (as well as single electron attachment and detachment electronic states of the same species) where comparison has been made with a closely related multi-reference coupled-cluster method, namely Intermediate Hamiltonian Fock Space Coupled-Cluster (IHFSCC) theory.