Relativistic effects are always present for all systems in so far as the theory of relativity is correct. There will always be a quantitative error when you neglect those effects. However, when we are considering chemical processes, those effects are generally quite small for lighter atoms.

Heavier atoms have more strongly charged nuclei and the electrons close to the nucleus have more kinetic energy. When you do or don't add relativity is always a decision based on the trade-off between computational complexity and the level of accuracy you want/need to obtain, which is also tried to the nature of the specific process you are studying, but as a rule of thumb for chemical processes, relativistic effects become "non-negligible" for species containing d-orbitals.

In practical terms based on my own work and reading, I think that the first and second row of transition metals should have relativistic effects included unless this isn't possible due to theoretical limitations, normally using an electron core potential (ECP) or pesudopotential. Heavier atoms should then start to be treated using relativistic quantum calculations based on Dirac's formulation such as the Douglas-Kroll-Hess (DKH) Hamiltonian, although using ECPs is still a possibility if the available theory is limited or it's important for the comparison with other calculations that the theory remain essentially consistent.

EDIT: For completeness, as Dwight correctly pointed out above, the "non-relativistic calculations" of light atoms that I'm comparing with, such as Hartree-Fock, Post Hartree-Fock, and Kohn-Sham Density Functional Theories, all include electron spin and produce antisymmetric wavefunctions, which I understand to be relativistic in origin.

thank you Dwight Walsh

i have another question related to relativity.

what is the impact of scalar relativistic formalism ?what's the the phenomena is correctly resolved if we implement scalar relativistic formalism? and what if we implement Dirac relativistic formalism what's resolved ?