Smiling and sporting a black eye, a homeless man with a "possible delusional disorder" has faced court over the bashing murder of a woman in an inner-Melbourne park.
Courtney Herron, 25, was found dead by dog walkers in Royal Park at Parkville on Saturday morning with injuries described by police as "horrendous".
Police arrested Henry Richard Hammond, 27, on Sunday and he faced Melbourne Magistrates Court on Monday on a single charge of murder.

Courtney Herron was found dead in a Melbourne park. Source: AAP
Ms Herron had been couch surfing and sleeping rough while struggling with drug and mental health issues at the time of her death.
Hammond also has no fixed address.
"It's a very tragic and complex situation," his lawyer Bernie Balmer said outside court after Hammond's brief appearance.
He told magistrate Donna Bakos that Hammond had a number of issues that would affect him in custody.
"There's a diagnosis of possible delusional disorder, possible autism spectrum disorder and historical diagnosis of ADHD," Mr Balmer said.
Hammond has previously taken medication to treat those conditions, including an antipsychotic prescription.
The magistrate ordered that he undergo a medical assessment.
Dressed in black, and without shoes, Hammond said nothing during the short court appearance.
With one black eye, he looked around the courtroom, sometimes smiling.
Prosecutor Madeleine Sargent originally asked for up to four months for police to compile their brief of evidence against Hammond.
A pathology report is still to be completed and officers are reviewing CCTV footage, she said.
Ms Bakos gave police until 5 August to prepare the documents and ordered that Hammond be remanded in custody until a committal mention on 16 September.

A message on a bouquet of flowers laid at the site where Courtney Herron's body was found in Royal Park, Melbourne. Source: AAP
'A horrendous attack'
"This was a particularly, particularly horrendous attack," Homicide squad Detective Inspector Andrew Stamper said on Sunday.
Inspector Stamper said she had been in sporadic contact with her family and there were "a lot of people out there who knew and loved Courtney".
"When there's a child that suffered drug use, mental health issues, family relationships can be fragmented," he said.
"That doesn't mean that families out there don't love their children, and you know, our heart breaks for them.
"We are dealing with a heartbroken family again."
Ms Herron's killing has sent shock waves among the wider Melbourne community with prominent and everyday Victorians outraged over the death of yet another young woman.
Over the weekend friends of Ms Herron and others laid floral tributes at the site where her body was found.
It was just a short distance from Princes Park, where the body of aspiring comedian Eurydice Dixon was found on 12 June last year.
Ms Dixon, 22, was raped and murdered. Aiia Maasarwe, 21, also died after being attacked while walking home near La Trobe University on 15 January.
Both women were attacked by men they did not know and who have since been charged.
Then in April, Natalina Angok's body was found dumped in Chinatown, allegedly killed by her one-time partner Christopher Allen who has since been charged.
The last confirmed sighting of Ms Herron was on 14 May at St Albans when she came into contact with the police.

Courtney Herron's body was found on Saturday in Parkville. Source: AAP
"Her mental health and her drug use (made) her particularly vulnerable," Detective Inspector Stamper said.
"This was a young woman who had significant challenges in life.
"We as a community should be protecting these people and we didn't. We failed on this occasion."
He said there was no evidence at this stage that the attack had been sexually motivated.

A man arrives to lay a bouquet of flowers at the site where Courtney Herron's body was found in Royal Park, Melbourne. Source: AAP
Men's behaviour
It came as Premier Daniel Andrews said men's attitudes to women need to change.
"This is a terrible tragedy," Mr Andrews told reporters on Sunday.
The Premier, who delivered Australia's first royal commission into family violence last term, said while the state had made significant progress on violence against women, there was more to be done.

Premier Daniel Andrews Source: AAP
"This is not about the way women behave. This is not about where women are at what hour," he said.
"This is most likely about the behaviour of men."
It's a sentiment echoed by Assistant Commissioner Luke Cornelius, who told reporters earlier that Melbourne was a safe city but attitudes against women needed to change.
"What is it in our community that allows some men to think that it's still OK to attack women or take from women what they want?" he said.
"Violence against women is absolutely about men's behaviour."
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