He's been taken in to be questioned/talked to/disapprovingly looked at and reprimanded. He'd had fines. He's spent a night or two in lock up, but so far they are afraid to out and out arrest him, and they have trouble proving he was actively looking for danger when he's out of costume. No, Steve is not in hiding.
SHIELD is doing the above, unless the hero is obviously out hunting for trouble/is less well known, then they will try to arrest or press charges. And if the heroes start bad mouthing them then...you'll see.