"As the matter is now before the coroner to make a determination regarding the circumstances of the death, police [are] unable to comment further."
Ms Thompson told Fairfax the news was "a huge relief".
"It has taken a long time to get to this. I knew that I hadn't done what I was suspected of doing, but it was still a bit weight off my shoulders," she said.
"I know the police have to do these things properly but I think three years was a bit long to put us through. It's a long time to have people thinking you might have done something you didn't do."
Ms Thompson said she hoped the end of the investigation might mean she could have more access to her children.
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