A man and a woman in their 70s were found dead at an address in the seaside town, police said.
Detectives are investigating the incident, which took place at a property in Anthony Avenue, Poole; Dorsetand it was reported on Tuesday at 11.35.
Police and an ambulance service went to the scene and the bodies of the pair were found inside the property, Dorset police said.
The man and woman were known to each other, their next of kin was notified and the coroner was notified, the force said.
DI Ian Allen said: “This is a very sad event and all we can do is support our neighbours.
“The teachers are carrying out inquiries to find out what happened and have a string in place to allow a thorough investigation of what happened.
“At this time, no one else is believed to be involved and investigations will continue to establish the full circumstances surrounding the murders.
“We are appealing for anyone who may have information to assist our investigation to please Dorset Police.
“We are trying to determine the timing of the events, but we are considering the time between the Christmas holidays and today.
“There will be an increased police presence in the area and we encourage anyone from the local neighborhood to contact the police team if they have any concerns or information.”
Anyone with information is asked to contact Dorset Police at www.dorset.police.uk or call 101, quoting incident number 55240198989.