Avon and Somerset Police has not named the man at the centre of the investigation, which began in December 2024.
It is being led by officers from Operation Bluestone, its dedicated rape and serious sexual assault investigation team.
“As a result of our enquiries, a file has been submitted to the Crown Prosecution Service to consider a charging decision,” the force said.
“We’ve updated the victims about this significant development, and we’ll continue to make sure they have access to any help or support they need.
“We’d respectfully ask people not to speculate on the circumstances so the investigation can continue unhindered.”
The Labour Party said it “immediately suspended” Norris after being made aware of his arrest.
The suspension means Norris has also had the party whip suspended, meaning he is not able to sit as a Labour MP in the Commons.
Despite his suspension, Norris has refused to step down from his position as an MP.
He is now sitting as an independent but has not attended the House of Commons since his arrest. He is still able to vote by proxy.
