Antibody tests are designed to have low false positives, not low false negatives.

And blood samples have found that a proportion of samples have t-cell immune responses to sars-cov-2 without antibodies, possibly with no exposure to sars-cov-2 specifically.

Specific antibody levels drop after a few months.

Therefore, might be impossible to establish if someone was exposed or what level of immunity.

There are specific tests that try to detect past infection, but the general standard tests will only detect current infection.