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A woman in her 40s was reportedly raped after leaving a pub.
The victim is believed to have left the premises in Charlton Green, Dover, in the early hours of Saturday.
Officers investigating have said she has limited knowledge of how she got home - which would have been passing through roads including Frith Road, Salisbury Road and Bridge Street.
The woman woke up later that morning at home but had facial injuries, including bruising, and has reason to believe she may have been raped.
She reported the incident to police and on Sunday a 41-year-old man from Dover was arrested on suspicion of rape.
He has since been released on police bail until August 14.
Members of the public have been urged to come forward with information.
Anyone who witnessed anything suspicious or who may have seen the woman walking through the particular Dover streets between midnight and 2am on Saturday should contact police.
Officers continue to investigate and have already reviewed CCTV and made a number of inquiries in the area.
Those with information should call 01843 222289 quoting reference 46/123383/20, or Crimestoppers anonymously on 0800 555 111, or by using the anonymous online form at Crimestoppers-uk.org.