Scanning tunneling microscopy (STM) can be used to detect inelastic spin transitions in magnetic nano-structures comprising only a handful of atoms. Here we demonstrate that STM can uniquely identify the electrostatic spin crossover effect, whereby the exchange interaction between two magnetic centers in a magnetic molecule changes sign as a function of an external electric field. The fingerprint of such effect is a large drop in the differential conductance as the bias increases. Crucially in the case of a magnetic dimer the spin crossover transition inverts the order between the ground state and the first excited state, but does not change their symmetry. This means that at both sides of the conductance drop associated to the spin crossover transition there are two inelastic transition between the same states. The corresponding conductance steps split identically in a magnetic field and provide a unique way to identify the electrostatic spin crossover.