Denishar Woods, 11, has been at Princess Margaret Hospital since touching the tap at the Beldon property on Saturday night.
Doctors informed her family earlier this week she had sustained brain damage.
Michael Bunko, a director at WA's electricity regulator, believed the tragedy was likely caused by a fault in the neutral conductor supplying power to the property.
While the incident was still being investigated, lawyers said the state government faced a potential multi-million dollar claim.
Premier Mark McGowan said it was too early to comment on that prospect.
"Those sorts of calls will be made in due course," Mr McGowan told reporters on Thursday.
"At the moment, we just want to support the little girl and the family."
Denishar's mother Lacey Harrison said she and her other six children were now scared to touch light switches or metal objects.
A spokesman for housing minister Peter Tinley said Ms Harrison had expressed interest in moving house.
"The Department has reserved a five-bedroom property for Ms Harrison and her family," he said.
"Ms Harrison has advised she would like to consider the property and the Department will continue to talk to her regarding her options."
The family was offered short-term motel accommodation, but were instead staying with relatives.
A GoFundMe crowdfunding campaign was launched to help the family.
