A photo of the weapon hanging from a door was sent via Twitter to five MPs, including Penistone & Stocksbridge MP Angela Smith.
The tweet, sent last week from an account called Sheffield and Yorkshire Direct Action Brexit Group, included the message: “We are ready for civil war…..are you?” A similar tweet was sent from another account.
South Yorkshire Police said two people were arrested yesterday afternoon in connection with the tweets and had since been bailed.
A spokeswoman for the force said: “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. Enquiries are continuing.”
The tweet was addressed to MPs Anna Soubry, Chuka Umunna, David Lammy, Angela Smith and Sarah Wollaston, all of whom have backed calls for a second referendum on leaving the EU, including the option to remain in the union.
The Star contacted Angela Smith’s office, which declined to comment on the tweets.
Twitter said it does not comment on individual accounts for reasons of privacy and security.
The offending tweet was yesterday removed from public view and it is understood Twitter placed the account in a read-only state until the user took action to delete the message.
Twitter states that it has a ‘zero tolerance policy against violent threats’, with anyone deemed to be sharing such messages facing ‘immediate and permanent suspension of their account’.
More than 150 people commented on the message before it was removed from public view, with many saying they had reported the matter to police.
Responding to criticism, a later tweet from the account insisted the crossbow message was not intended to be threatening.
The follow-up tweet declared: “Threatening to kill?????? How? All used to protect my home and my family, just indicating that whatever happens with Brexit, when law and order goes to **** I and my 'terrorist network cell' (you’re an idiot) will be ready! Will you?”
A further tweet from the account stated: “I’m a caring kind of person. Just want my MPs to be careful that nothing happens to them.”
And another said: “It’s OK, don’t bother wasting your energy. Everyone has reported me and.....shock horror......no police....no Twitter ban.”