A 44-year-old woman, nine-year-old boy and five-year-old girl all died when their motorhome collided with a parked HGV near the Jinnah restaurant, Harton, on August 24.
The father, who was driving, and his six-year-old son were seriously injured but have now been released from hospital.
The victims have not been named by police or by family members and an inquest into their deaths has not yet opened. They are believed to be from Yorkshire.
However Sergeant Paul Cording has now revealed that the man and his son returned home from hospital to find that their house had been ransacked by burglars.
He has set up a Gofundme page with a £1,000 target which has already been exceeded by £800.
Sergeant Cording wrote: "You may be aware of the tragic incident we attended on the A64 at Harton in which three members of the same family sadly died at the scene. The good news is that the six year old boy seriously injured in the RTC has been allowed home with his dad which is fantastic news.
"Unbelievably though when the young lad and his dad returned home they found their house had been burgled and the thieves had taken everything, including items such as a TV, Xbox and sentimental things that can never be replaced. Both the RTC and the burglary are ongoing investigations and I will therefore not comment on those but myself and my team (along with other 999 colleagues) are horrified with what has taken place and can’t just sit by & do nothing.
"We have started a collection to replace some of the items and if you would like to help this family try to rebuild their lives then please do donate if you can."
To donate, click here.