There exits a communication between cells, and so there must exist an electrical resource.I suspect it could be Na and K ions partitioned by cell membrane.
The communication between cells is by signal molecules, e.g. chemically. The first type of signalling is endocrine, when a signal molecule is released into the blood stream of an organism. The second type is paracrine in which the signal molecule diffuse by some mediator to the surrounding cells. The third type is communication in between neuronal cells. The signal in between neurons is again on transmitted on chemical basis by release of the neurotransmitter in gap between the two neurons.
Completely different story is the propagation of the signal along a single neuron. The propagation of the so called action potential is performed by fluxes of ions across the outer membrane of the cell. The voltage across the membrane is built up. However this voltage does not do any communication between cells.
Ionic imballance across membranes and hence membrane voltage is actually very common and crutial for life. Na+/K+ ATPase makes ATP and runs on gradient of protons across the plasma membrane for example.