42 U.S.C Section 1983 is the law. It was enacted in the Civil
Rights Act of 1871. When you sue an official under Section 1983,
you are usually suing for violation of a constitutional right, not
a statutory one, so there aren't a lot of laws to consider but
there are a lot of court cases. There are a lot of exceptions to
1983, including absolute immunity for legislators, court witnesses,
etc, and qualified immunity for executive officials. All of these
come from cases, not laws.
The liability was under federal law to answer your exact
question.