If you are intentionally or unintentionally happen to have your rabbit on its back, it’s probably tranced, which is very bad. Now rabbits sometimes accidentally trance themselves as they jump and fall about, and it may look “relaxed”, but it’s actually the highest tier of fear: faking death so a predator leaves. It’s a highly stressful and exhaustive state that comes off as relaxed, but isn’t actually.
In other situations, rabbits are quite good at deciding “I’m relaxed so I’m going to partially fall asleep now” and they just are not moving or react to stimuli right away at all. The indicative marker is eye size. Wide eyes is always alertness, while relaxed eyes is relaxation and asleep. When a rabbit is actually asleep, their eyes may get big, but they begin moving and you see the pupil change in size as they go through a dream state. When they’re wide eyed out of fear, it’s a much more deliberate eye motion of huge pupils looking for the source of their fear.
The answers provided in this discussion are for general guideline purposes only. The information is not intended to diagnose or treat your pet. Seek the advice of your veterinarian or a qualified behaviorist.