A nanoscale molecular switch can be used to store information in a single molecule. Although the switching process can be detected electrically in the form of a change in the molecule's conductance, adding spin functionality to molecular switches is a key concept for realizing molecular spintronic devices. Here we show that iron-based spin-crossover molecules can be individually and reproducibly switched between a combined high-spin, high-conduction state and a low-spin, low-conduction state, provided the individual molecule is decoupled from a metallic substrate by a thin insulating layer. These results represent a step to achieving combined spin and conduction switching functionality on the level of individual molecules.