Officers were first alerted to an incident at the Weighbridge Taxi Rank, at about 00:25 on Sunday 3 November.
While at 01:00, officers said an incident occurred between two women near the side entrance to Boots on the Pier Steps and one was assaulted.
Any witnesses to either incident should call Guernsey Police on 725111 or Crimestoppers anonymously on 0800 555 111.
Pictured: The Weighbridge Taxi Rank and Guernsey Police Station.