We have carried out a systematic first-principles study of muonium (μ+e-) adducts in A- and B-form DNA. Potential trapping sites in the bases cytosine and thymine were considered. Our results indicate that the difference in structural geometry between A- and B-form DNA can lead to substantial deviations in the hyperfine fields at the μ+ sites. This could have important implications for the interpretation of muon spin relaxation measurements that have shown evidence for an enhanced electron mobility in A-form DNA, but implicitly assume a negligible difference in the magnitude of the hyperfine fields at the trapped μ+ site between A- and B-form DNA.