Police have confirmed that Yasser Alromisse lived in Broomfield Avenue, Worthing, at the time of his death on Thursday.
He shot his seven-year-old daughter Mary Shipstone in the head, outside her home in Spring Hill, Northiam, shortly before 4pm on Thursday.
She was taken to King’s College Hospital in London but died at 2.56pm on Friday, September 12.
Police spent much of Friday door-knocking at the Broomfield Avenue home.
Detective Chief Inspector Jason Taylor said: “This is a fast-moving investigation and there are still a large amount of inquiries being carried out before we can confirm the full picture of what happened.
“We are currently trying to establish Mr Alromisse’s movements over the last few days and are keen to hear from anyone who may have seen or heard from him.
“At this time however, I am not looking for anyone else in connection with this investigation and believe this to be an isolated incident.”
Resident Michael Cloake, said: “There is a permanent police presence. There were three cars last night and one on site all the time. We didn’t know the man but I think he lived a few doors down. He kept himself to himself. It’s a very quiet area and a friendly neighbourhood. It is a shocking and sad tale.”
It has been suggested that the estranged couple were in a dispute over custody.