The allegations involve men in their twenties.
Evans later announced he was leaving his role as deputy speaker, but maintained his innocence.
"Whilst I'm saddened this case has not been closed today, I am certain of two things: firstly that I am innocent; and secondly, that my innocence will be demonstrated," he said after leaving Preston police station in north west England.
"Having informed my fellow deputy speakers Lindsay Hoyle and Dawn Primarolo, my association chairman and my staff, I can confirm I will now resign as deputy speaker."
However, he revealed that he would remain an MP.
At the time of the original allegations, Evans dismissed them as "completely false", saying they had been made by two people he had "regarded as friends".
In June he said: "I continue to refute all allegations."
Evans was one of three deputy speakers elected in a secret ballot of MPs in 2010 and later that year revealed he was gay, saying he was "tired of living a lie".
- AFP