Retinal bipolar cells are known to have resting potentials from which they can become more or less polarized. What I'm wondering is whether a bipolar cell's neurotransmitter-release rate is zero when it's at resting potential, or whether it's zero when it's fully hyperpolarized.
Bipolar cells reduce transmitter release when hyperpolarized, see the wikipedia page. When the bipolar cell is fully hyperpolarized it will basically stop releasing neurotransmitters. If transmitter release ever becomes totally zero I do not dare to say, however.