PC Ben Jones said the incidents had taken place in Whitchurch in recent weeks, and has issued a description of an individual as part of the investigation.
He has asked for the public to share any CCTV footage, or video from Ring Doorbells, that might show the person.
He said: "We would like to hear from anyone who has had any malicious notes left on their vehicles.
"Regardless of whether you have received any malicious communications, we nevertheless want to ask that you review any CCTV footage, including that captured with a ring doorbell between the following times: 3.30pm to 4.30pm on November 25; 8.30am to 9.45am on November 28; 3.45pm to 4.45pm on December 2; 2.45pm to 3.45pm on December 5.
"We are specifically requesting any footage where the following description of a person is seen: Figure wearing a black puffer coat, with a black fur hood up, black bootleg trousers and black shoes."
Anyone with information can contact PC Hewins on firstname.lastname@example.org