They say it happened in the early hours of Wednesday 16 March, at Columbus Street Corner Shop.
Officers believe the thief broke in, before stealing cash, scratch cards and the charity boxes.
They have now issued the above photos of a person they are looking for, which were taken on CCTV.
Anyone with information is asked to contact police on 612612 or the independent charity Crimestoppers anonymously on 0800 555 111 or via their Anonymous Online Form at Crimestoppers-uk.org.
Picture Credit: States of Jersey Police.