Crustal magnetic fields influence a range of plasma processes at Mars, guiding the flow of energy from the solar wind into the planet's atmosphere at some locations while shielding the atmosphere at others. In this study we investigate how the topology of crustal fields varies with changes in the direction of the incoming interplanetary magnetic field (IMF). Using plasma measurements from Mars Atmosphere and Volatile Evolution (MAVEN) and Mars Global Surveyor (MGS), we identify magnetic topology throughout the Martian ionosphere and perform a statistical analysis of crustal magnetic field topology during different IMF configurations. We find that the topology of crustal field cusp regions is dependent on IMF direction and that cusps transition between open and closed topology regularly as they rotate through the nightside of Mars. Finally, we determine that cusps often become topologically closed due to reconnection with open magnetic fields in the Martian magnetotail, creating large closed loops that connect the dayside and nightside of Mars.