Rabbits love twigs and branches to help wear their teeth down, make sure you avoid trees that have fruit with stones, such as cherry or plum as these are toxic. Plants and shrubs from the garden can also be dangerous and so should be avoided.
Poisonous plants and shrubs:
Lily of the valley,
All ivy plants,
Safe options are rowan, pine, aspen and birch trees. Twigs from apple and pear trees are safe, as well as branches and leaves from currant, raspberry and blackcurrant that are tasty and safe to offer. Avoid anything that grows from bulbs, or has been treated with insecticides, fungicides or other toxic products.