Lori Klausutis,28,died in 2001 after fainting and hitting her head while working in a Florida regional office for Scarborough,then a congressman,who is now the host of the MSNBC news programMorning Joe.
Trump,a frequent target of criticism from Scarborough,has tweeted in recent weeks seeking to revive false conspiracy theories linking Scarborough to her death.
"When will they open a Cold Case on the Psycho Joe Scarborough matter in Florida,"he tweeted on May 12.
No evidence exists connecting Scarborough to the woman's death and authorities concluded long ago that it was an accident.
Trump defended himself with a new set of tweets saying"the opening of a Cold Case against Psycho Joe Scarborough was not a Donald Trump original thought,this has been going on for years".
Twitter issued a statement saying it was"deeply sorry about the pain these statements,and the attention they are drawing,are causing the family,"but did not address the question of whether it would remove Trump's tweets.