Officers say stalking reports allege he left at least three packages at the door of a home in the town.
The last delivery, to the same address, was caught on camera on December 29 at around 7:10 p.m. – again the suspect had their face covered.
A spokesperson from Sussex police said: “Enquiries into these incidents are ongoing, and we are asking anyone with information to report it to police.
A series of reports of concerning behavior, which span a year, prompted the investigation, in Hailsham Sussex, England.