Well the easter bunny makes as much sense as
this does.
But perhaps the easter bunny is a female bunny gone mad, as she cannot get any offsprings, due to being sterilized after a surgery, when she had cancer somewhere private... So she is somewhat jealous of others getting offsprings, like chickens. And go out during the night to take their eggs.
But when she got officer Rooster on her ass, she now had to start hidding the evidence, by dumping the eggs in peoples gardens, making us the guilty ones.
Or the bunny simply just suffer from cleptomania.