The Church was criticised for making the new investigation public, with Lord Carlile calling the decision "unwise, unnecessary and foolish".
The police statement suggests that their investigation closed more than a month ago without the public being told.
It is also not known whether Bishop Bell's niece and only surviving relative Barbara Whitley, 94, was informed.
In a statement the police force said: "On Tuesday 30 January this year we received information from the Church of England concerning an allegation made against the late Bishop George Bell.
"The information was assessed and a proportionate investigation has been carried out to clarify the circumstances.
"This was done thoroughly and sensitively, although of course further police investigation or action is not possible as Bishop Bell died 60 years ago.
"There are no current safeguarding issues.
"The matter is now closed as far as Sussex Police are concerned and the Church of England have been informed of this."
Andrew Chandler, Bell's biographer and founder of the George Bell Institute, said: "'In October 2015 the Church authorities were prepared to devastate the name of a dead man on the basis of a wholly discreditable process.
"In January 2018 they were ready to do so on the basis of no process at all. I imagine they regard this as progress.
"At all events, this statement reinforces a sense that the making of allegations is more important to the Church than the testing of them.
"It also shows how the church authorities are prepared to exploit the arts of publicity in their own interests."
Dr Ruth Hildebrandt Grayson, the daughter of Bishop Bell's friend Franz Hildebrandt, said: "I doubt there was any new information. I think it was probably a smokescreen or a stalling tactic.
"The Carlile report did not go their way and I think they were scrabbling around for anything more which could be found which would justify the way they have tried to blacken George Bell's name, and they have failed."
A spokeswoman for the Church of England said: "Fresh information was received regarding Bishop Bell following the publication of the Carlile Review in December.
"In January the National Safeguarding Team announced that it was commissioning an independent investigation into this information and we cannot make any further comment until the investigation is completed."
A representative for the Archbishop of Canterbury has also been approached for comment.
