A model has been developed to investigate the transport of the upward flowing ionospheric ions from closed field lines of the Martian day and nightside ''polar'' magnetosphere into the solar wind interaction region. Guiding center ion trajectories in the polar regions, for a range of injection conditions of the convection electric field, gravitation, and magnetic gradient force using a simplified three-dimensional magnetospheric model were calculated. The dependence of the heavy ion escape on the Martian magnetopause positions and the solar wind ram pressure was also investigated. The calculated parallel escape fluxes of molecular ions are in good agreement with the Phobos 2 measurements and other theoretical calculations. Our investigation of molecule ion escape from high latitudes strongly suggests the presence of a weak intrinsic magnetic moment, (estimated to be about 1022 G cm3), since only then are molecular ions capable of reaching the solar wind interaction region. The detailed properties of a Martian magnetic field, however, should become known from the magnetometer measurements on the forthcoming Mars Observer mission.