Here, we do not require a permit for carpet, or any other floor coverings. And as far as debris clean-up, all you need is a verbal approval for a dumpster location from zoning, as to it not being on the public street.
Personally, from super storm Sandy, we were told to put all damaged items on the curb, and the Township provided pickup and disposal (Brick Township). They took everything.
That is the way it worked here. Pile it on the curb, they come get it. A few guys abused the system and tore their houses down, piling it all on the curb. They traded a $40,000 demo bill for a weekend of machine time.