South Hams MP Sarah Wollaston was one of five MPs subjected to a series of threatening tweets, including one which contained a reference to the murdered Labour MP Jo Cox.
The tweets appeared on an account called the Sheffield and Yorkshire Direct Action Brexit Group.
One of the tweets, addressed to Labour MP David Lammy plus Independent Group MPs Anna Soubry, Chuka Umunna, Angela Smith and Dr Wollaston, said: “We are ready for civil war…. are you?”
One tweet called Ms Soubry a “traitor” and said “remember what happened to Jo Cox”. Another included a picture of a crossbow.
South Yorkshire Police said on March 27: "Investigations are ongoing after a series of threatening social media posts directed at Members of Parliament were reported to us earlier this week.
“A 40-year-old man and a 33-year-old woman were arrested in Sheffield yesterday on suspicion of sending malicious communications.
“They have since been released on bail.
“Inquiries are continuing.”
The Twitter account has now been closed for violating rules against abusive behaviour.