A homeless man accused of killing 25-year-old Courtney Herron in a Melbourne park has a "possible delusional disorder", his lawyer has told a court.
Henry Richard Hammond, 27, faced Melbourne Magistrates Court on Monday, after being charged overnight with murdering Ms Herron, whose body was found in Royal Park in the city's inner north on Saturday morning.
It's alleged she was killed earlier that day. Hammond looked around the courtroom, smiling occasionally, during the brief court hearing.
He wore black and had bruising on his face, including a black eye.
His lawyer Bernie Balmer said Hammond had custody management issues.
"There's a diagnosis of possible delusional disorder, possible autism spectrum disorder and historical diagnosis of ADHD," he said.
Prosecutor Madeleine Sargent originally asked for up to four months for police to put together their brief of evidence against Hammond.
A pathology report is still to be completed and officers are reviewing CCTV footage.
Magistrate Donna Bakos said police could have until August 5 to prepare the documents and ordered Hammond, of no fixed address, be remanded in custody until a committal mention on September 16.