Graffiti has been spray-painted on several buildings around West Centre and Ann Street.
The tags 'POSH' and 'AMS' were painted more than 60 times in black or pink paint on Saturday evening (26th October) into Sunday morning (27th October).
Police want to speak to anyone who saw what happened and has any information on who did this.
The force is also keen for information on the significance of the tags.
Anyone with information is asked to call police on 612612 or Crimestoppers anonymously on 0800 555 111.

Social worker tribunal concludes
Deadline set to bring forward Jersey's whistleblowing law
Tonight's Sanctuary Trust Sleep-out marks 15 years of its homelessness support
Microsoft suffers global outage - as fix not going 'as expected'
David Walliams’ books to remain available in Jersey Library and schools
One in three homeless people in work
Fort Regent vision 'was never matched' by a budget that could deliver it, says JHA
Buzzing! Bears and Bees coming to Jersey