Try Online Searchable Death Indexes & Records. http://www.deathindexes.com/

Since what you are looking for is after 1961, there may be a fee if it is listed. I have discovered that not all family members have obits in the newspaper, but you will at least be able to know if there is one.

If you are looking for a grandparent, etc., I have asked a closer family member to request the death record by mail with success.