Ms Searle's son, the country musician and former Hollyoaks star Callum Kerr, said in an Instagram statement on Saturday that he and his sister Amanda Kerr and Mr Searle's two children, Tom and Ella Searle, were grieving.
Ms Searle's body was reportedly found outside their home with a head injury, with jewellery found scattered nearby, while Mr Searle's body was discovered inside the house hanged and gagged, according to local media.
Andrew Searle, 62, and Dawn Searle, 56, are reported to have been found dead by a German friend, who lives nearby, after Mr Searle didn't arrive for one of their regular dog walks.
Investigators are reportedly looking at whether the British couple was killed during a burglary, but all lines of inquiry - including murder-suicide or potential links to Mr Searle's previous work as an organised crime financial investigator in the UK - are open.
Speaking to Sky News from the town hall in which he conducted the couple's wedding ceremony, he said: "It doesn't seem like the problem comes from here because when we knew them and saw them living here they were very happy, very friendly and didn't seem to have any problems.
