Colin Barnett says he will contact the attorney-general to speed up police and health department enquiries into the death of 22-year-old Indigenous woman, Julieka Dhu.
Ms Dhu died on August 4 after she spent three days in the Port Hedland watch house two months ago.
It is understood she was in custody because she owed about $1000 in unpaid fines.
Police said at the time that after complaining of feeling ill, she was taken to hospital three times and died on the final visit.
Mr Barnett said it was a "very tragic situation" and he was keen to see a coronial report completed as soon as possible.
"The cause of death, I understand, was a heart attack. What led to that I think we need to know," he told ABC radio on Thursday.
The premier said he would speak with Attorney-General Michael Mischin about the matter as soon as possible, but said he would not interfere with the coronial process, which should be independent.
"I want to see this resolved quickly. I think a lot of people are jumping to conclusions, which may not be true," he said.
A police spokeswoman told AAP that inquiries were continuing and it was envisaged the completed file would be forwarded to the coroner by the end of the month.
The Health Department was also looking at what happened when Ms Dhu was treated at the Hedland Health Campus, Mr Barnett said.
- With AAP
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