The dealership normally registers the vehicle for you by providing all the evidence and your registration request to the DMV. In this case, you don't need to do anything else
What happens if I don't pay New York State sales tax to the leasing company?
in that case please provide your lease, and the complete Statement of Transaction {Sales Tax Form} PDF in the New York State Department of Taxation and Finance DTF-802. You must pay New York State sales tax at the DMV office on any lease payments if the leasing company or dealer did not collect the sales tax.
What happens if I don't pay New York State sales tax to the leasing company?