The incident happened at around 2pm on Tuesday 1 June 2021.
It is reported a man was sitting on a bench in Brenchley Gardens near Station Road, when he committed an indecent act.
Sergeant Andrew Ferguson said: ‘We understand there were a number of families in the park at the time and we would like to speak to anybody who witnessed a man acting suspiciously or indecently.’
Any witnesses are urged to contact Kent Police on 01622 604100, quoting reference 46/93621/21.
You can also contact Kent Crimestoppers anonymously on 0800 555111 or by using the online form on their website.
A local man in his 70s was later arrested on suspicion of indecent exposure and was released pending further investigation.