The mirror dark matter ( MDM ) model of Berezhiani et al . has been shown to reproduce observed galactic rotational curves for a variety of spiral galaxies , and has been presented as an alternative to cold dark matter ( CDM ) models . We investigate possible additional tests involving the properties of stellar orbits , which may be used to discriminate between the two models . We demonstrate that in MDM and CDM models fitted equally well to a galactic rotational curve , one generally expects predictable differences in escape speeds from the disc . The recent radial velocity ( RAVE ) survey of the Milky Way has pinned down the escape speed from the solar neighbourhood to v _ { esc } = 544 ^ { +64 } _ { -46 } km s ^ { -1 } , placing an additional constraint on dark matter models . We have constructed an MDM model for the Milky Way based on its rotational curve , and find an escape speed that is just consistent with the observed value given the current errors , which lends credence to the viability of the MDM model . The Gaia-ESO spectroscopic survey is expected to lead to an even more precise estimate of the escape speed that will further constrain dark matter models . However , the largest differences in stellar escape speeds between both models are predicted for dark matter dominated dwarf galaxies such as DDO 154 , and kinematical studies of such galaxies could prove key in establishing , or abolishing , the validity of the MDM model .