I checked RootsWeb's version of the online Social Security Death Index :
http://ssdi.rootsweb.comThere is a listing for a Dorothy E. HARRINGTON, who lived from 1916 to 1994. Her last residence was in Paducah, KY.
It's your judgment as to whether that is the right person. Earlier today, on this board, I have discussed research into the death certificate, and you can consider applying for hers.
Reg Niles
RegNMINiles@cs.com