If the vehicle is older than 15 years, you don’t need a title. Otherwise, the required application form is at the link http://dmv.vermont.gov/sites/dmv/files/documents/VT-004-Replacement_Title_App_0.pdf
If a damaged title is being replaced, include the original damaged title.
By mail. Send the completed form along with $35 fee to Department of Motor Vehicles, 120 State Street, Montpelier, VT 05603-0001
In person. Bring the form to the Montpelier office located at 120 State Street, Montpelier Vermont 05603. You will also need form http://dmv.vermont.gov/sites/dmv/files/documents/VT-016-Personal_Delivery_Of_Title.pdf
REPLACEMENT TITLE – VERMONT
You cannot transfer ownership of your vehicle if you do not possess the Title Certificate. The most common reason you would not possess the Certificate is that there is a lienholder (lender) for the vehicle. In this case the lien holder maintains control of the title until the lien (loan) is paid off. This common situation does not require a replacement of the original title, but instead a transfer of the title to you.
REPLACEMENT. The title must be “replaced” if the original has been lost, damaged (rips, coffee stains, water damage), has cross outs or white outs, or has incorrect entries (such as seller’s printed name and signature not matching the official names on the front of the title) or signatures in the wrong place.