The late-time tail behaviour of massive scalar fields is studied analytically in a stationary axisymmetric EinsteinMaxwell Dilaton-Axion (EMDA) black hole geometry. It is shown that the asymptotic behaviour of massive perturbations is dominated by the oscillatory inverse power-law decaying tail t-(l+3/2) sin(μt) at the intermediate late times, and by the asymptotic tail t-5/6 sin(μt) at asymptotically late times, with μ being field mass. Our result seems to suggest that the intermediate tails t-(l+3/2) sin(μt) and the asymptotically tails t-5/6 sin(μt) may be a quite general feature for evolution of massive scalar fields in any four-dimensional asymptotically flat rotating black hole backgrounds.