We provide a theory of the electronic transport properties of a graphene layer functionalized with molecular switches. Our considerations are motivated by the spiropyran-merocyanine system which is non-polar in its ring-closed spiropyran form and zwitterionic in its ring-open merocyanine form. The reversible switching between these two isomers affects the carriers in graphene through the associated change in the molecular dipole moment, turning the graphene layer into a sensor of the molecular switching state. We present results for both the quasiclassical (Boltzmann) and the quantum coherent regimes of transport. Quite generally, we find a linear sensitivity of the conductance on the molecular dipole moment whenever quantum interference effects play an essential role which contrasts with a quadratic (and typically weaker) dependence when quantum interference is absent.