Armed police were called to a Post Office following reports of an attempted robbery.
Officers arrived at the shop in Twydall Green, Gillingham, shortly after 2.50pm.
It is alleged threats had been made to a member of staff before a man fled the scene empty-handed.
Patrols, including armed officers, attended but the suspect had left prior to their arrival.
Nobody was harmed during the incident and a search of the area was carried out.
Investigators are appealing to any witnesses to contact the appeal line on 01634 792209, quoting reference 10-0790.
