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Teancum Vernon Petersen-Crofts was charged after the woman and her son were found dead and her daughter was found critically injured at a house in Ellenbrook, about 30 kilometres north-east of the city centre, in the early hours of Sunday morning.
The teenage girl was taken to hospital but died on the way.
Appearing in Midland Magistrates Court in handcuffs and flanked by two security guards, Mr Petersen-Crofts began talking confusingly over the magistrate.
Referring to a person named "Griff" or "Griffin", the teenager said "he's a criminal" who "wanted to take me out bush".
"He did it and he came back for my family," Mr Petersen-Crofts said.
"I ran away from him and went back home.
"He came back for my family. Mama is with me."
Magistrate Greg Smith asked Mr Petersen-Crofts to stop talking, but he ignored the request and continued with his outburst.
"I was painting a picture of Jesus … Mama told me to save myself," he said.
"He looks like a serial killer and he's a security guard."
