You can let it stay in you're yard and put some food out for it. Rabbits love dandelion greens, hay you can put some rabbit pellets out, but if it's wild let it be out side I had rabbits for pets and also had a family of wild ones out side I used to leave some food and fresh veggie goodies for it. Got to the point after a while the one never ran from me while i was out side and would wait for me to leave food for them
It should run away from you if it is wild, so in that case leave it in your backyard... But if it comes to you then it is used to human contact so most likely is a lost pet.. So take a picture and put up signs
No need to capture it, we have a bunny that comes and goes. He is sometimes in the backyard or in the front lawn. We will not see him for a few days and he will always manage to come back. You dont have to capture it, if you want it as a pet give it food like lettuce or carrots when you see it and it will come to you. After a while the bunny rabbit will get used to you and not run away from you. Just don't try to chase it because then he will never get used to you.
You can capture it if you wanna play with it or something, but other than that, you don't HAVE to. If you do, make sure you take care of it good cuz people just throw carrot sticks at rabbits like they're nothing and the carrot stick that they threw ended up hitting the bunny's head and blood came out. Jk.