The the required Application For Duplicate Certificate of Title form is at the link http://www.dmv.nebraska.gov/dvr/pdf/dupttlapp.pdf If more than one registered owner is on the title, both must sign (A spouse may represent the other spouse, however). All signatures must be NOTARIZED.
Bring the documents to your County Motor Vehicle Office (County Treasurers) which can be found at http://www.dmv.nebraska.gov/dvr/mvtitles/ctyofflist.html The Fee is $14.00.
RELATED LINKS:
TITLE INSTRUCTIONS FOR SELLING A CAR IN NEBRASKA
REPLACEMENT TITLE – NEBRASKA
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.