The required application form for a replacement (duplicate) title is available at the link http://dor.mo.gov/forms/108.pdf Above the “OWNER” section be sure to check the box above that section that says (DUPLICATE). For duplicate title you must have the form NOTARIZED.
If the the original title is damaged, you will submit it along with the application. Mail documents along with a check or money order for $10 to Motor Vehicle Bureau, PO Box 100, Jefferson City, MO 65105-0100.
Or, bring it to your local MVB office. Locations can be found at http://dor.mo.gov/offloc/
NOTE: If there was a lien shown on your original title and you paid it off, you will also have to submit a NOTARIZED Lien Release (DOR-4809). Form is at http://dor.mo.gov/forms/4809.pdf
RELATED LINKS:
TITLE INSTRUCTIONS FOR SELLING A CAR IN MISSOURI
REPLACEMENT TITLE – MISSOURI
You cannot transfer ownership of your vehicle if you do not possess the Title Certificate. In Missouri the registered owner of the vehicle is the one who maintains possession of the paper title.
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.