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The incident is reported to have happened between 2.45pm and 4.30pm on Tuesday 28 December 2021 in Oakwood Cemetery, near Oakapple Lane.
The victim and the man, who are known to each other, walked into the cemetery before he is alleged to have assaulted her.
Following enquiries investigating officers are appealing for witnesses to the incident, which is being treated as isolated.
In particular, police would like to talk to a woman who was seen walking two dogs in the same area at the time of the incident.
Officers have since arrested a man in connection with their enquiries. He has been bailed until Sunday 23 January 2022 while further enquiries are carried out.
Anyone with information is urged to contact Kent Police on 01622 604100 quoting crime reference 46/YY/266611/21.
You can also call the independent charity Crimestoppers anonymously on 0800 555111 or complete their online form.