A man has been arrested after reports a woman was raped.
It is alleged to have happened at around 8.30pm last Sunday (October 27) in Gillingham Park, near the Canterbury Street entrance.
Following initial enquiries, officers arrested a man the following day.
The 43-year-old from Gillingham remains in custody.
Police are continuing to pursue several lines of enquiry to establish the full circumstances.
This includes forensic analysis at the scene and checks for CCTV opportunities.
Officers would like to hear from anyone who may have been in the area between 8pm and 9pm, or have information which could assist the investigation.
Contact Kent Police on 01634 792209 quoting reference 46/182580/24.
You can also call Crimestoppers anonymously on 0800 555111 or complete their online form.