It depends. If your building doesn’t require one, then the worst thing that will happen is that the movers will damage something in the building and you will be held liable for the cost of repair. As well, if one of the movers gets injured during the move and the company doesn’t have worker’s compensation, you might be on the hook to pay for their hospital fees! If your building does require one, it might mean that you can’t move in or out that day as most buildings turn anyone away who hasn’t submitted the COI.