
The concerned party sends information via email or snail mail. After verifying the information Twitter either removes the account of the descended person entirely or provides archive of all that user's tweets so that the family members might access them offline. However, Twitter has introduced a new policy that every Twitter user needs to know. In case you have a family member or close-one on Twitter who has descended, here's what you need to do .
Follow the given steps to go for either choice (close the account or achieve it)
* Users full name, contact information (including e-mail address), and your relationship to the deceased user.
* A link to the profile page of the Twitter account or the username of the Twitter account
* A link to a public obituary or news article.
source: http://blog.taragana.com/index.php/archive/how-to-close-or-archive-twitter-account-of-a-deceased-member-under-new-user-policy/