Context: .The chemically peculiar HgMn stars are a class of Bp stars which have historically been found to be both non-magnetic and non-variable. Remarkably, it has recently been demonstrated that the bright, well-studied HgMn star ? And exhibits clear Hg ii line profile variations indicative of a non-uniform surface distribution of this element. Aims: .With this work, we have conducted an extensive search for magnetic fields in the photosphere of ? And. Methods: .We have acquired new circular polarisation spectra with the MuSiCoS and ESPaDOnS spectropolarimeters. We have also obtained FORS1 circular polarisation spectra from the ESO Archive, and considered all previously published magnetic data. This extensive dataset has been used to systematically test for the presence of magnetic fields in the photosphere of ? And. We have also examined the high-resolution spectra for line profile variability. Results: .The polarimetric and magnetic data provide no convincing evidence for photospheric magnetic fields. The highest-S/N phase- and velocity-resolved Stokes V profiles, obtained with ESPaDOnS, allow us to place a 3? upper limit of about 100 G on the possible presence of any undetected pure dipolar, quadrupolar or octupolar surface magnetic fields (and just 50 G for fields with significant obliquity). We also consider and dismiss the possible existence of more complex fossil and dynamo-generated fields, and discuss the implications of these results for explaining the non-uniform surface distribution of Hg. The very high-quality ESPaDOnS spectra have allowed us to confidently detect variability of Hg ii ? 6149, ? 5425 and ? 5677. The profile variability of the Hg ii lines is strong, and similar to that of the Hg ii ? 3984 line. On the other hand, variability of other lines (e.g. Mn, Fe) is much weaker, and appears to be attributable to orbital modulation, continuum normalisation differences and weak, variable fringing.