  A theoretical analysis is made of experiments in hydrogen and antihydrogen
that test CPT. We show that these experiments also provide sensitive tests of
Lorentz symmetry for protons and electrons. Both 1S-2S transitions and Zeeman
hyperfine splittings in the ground state are examined. We find that sensitivity
to CPT and Lorentz violation at the level of $10^{-27}$ GeV is attainable.
