Chief Inspector Lindsay Tulloch has said that there will be a “continued police presence” this weekend.
This comes after the deaths of Tracey Walker in Ladies Drive, and Peggy Griffiths in a house explosion in Brae earlier this week.
Mr Tulloch said that “locally based officers and specialist resources from elsewhere in Scotland” would be on patrol over the weekend, and would be carrying out “ongoing enquiries” in relation to the incidents.
“This past week has seen a number of high profile and tragic incidents in Shetland which we know has had a considerable impact on our island community.
“Incidents such as we have seen this week are extremely rare in Shetland and I would like to place on record our gratitude to local residents who have been incredibly supportive of the police investigations.
“You may see a continued police presence over the coming days”.
Mr Tulloch also thanked the people of Shetland “for their patience and understanding during this period”.
“My sympathy and thoughts are very much with those directly affected and their families.”