The family of the Melbourne pastry chef allegedly raped and murdered in Kings Domain has thanked the community and police for their support.

Victoria Police released the statement on Friday afternoon from Renea Lau's Hong Kong-based family.

"We are thankful for the media's concern and the community's support in relation to the death of Renea," the statement read.

"In the meantime we need some time and ask for privacy as we go through such a hard time in our family.

"Our family especially thanks and appreciates the effort of Victoria Police on their efficient investigation. Lastly our family wishes all Melbournians having a happy life here."

Ms Lau, 32, was walking to work on St Kilda Road last Saturday morning when she was allegedly chased and attacked in Kings Domain.

Scott Allen Miller, 42, was charged with her rape and murder and was remanded in the Melbourne Magistrates Court on Wednesday for a committal mention on October 24.

Ms Lau was a highly-skilled pastry chef at a dessert business in Melbourne's inner-east.