Margaret Thornton was last seen with her dog in the village of Upper Halling, near Snodland, at around 10am on Sunday 4 September 2022.
The 69-year-old is described around 5ft tall, with short, straight, blonde hair.
She is believed to have been wearing dark trousers and a pale jumper when last seen and was walking a small, black and tan terrier.
Officers are concerned for her welfare and ask anyone who has seen her or knows of her whereabouts to call 101, quoting reference 04-0700.
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