No woman should change their behaviour following the death of Eurydice Dixon in a Melbourne park this week, the Premier has said.

In a strong statement on Facebook, Daniel Andrews has ramped up debate about the safety of women in Melbourne and their need to protect themselves at night.

"Our message to Victorian women is this," Mr Andrews wrote. "Stay home. Or don't. Go out with friends at night. Or don't. Go about your day exactly as you intend, on your terms. Because women don't need to change their behaviour. Men do."

"She was just wonderful": Eurydice Dixon.

In the hours after the 22-year-old budding comedian died on a soccer pitch in Carlton North this week, police were concerned that it might be linked with another sexual assault in nearby Parkville and urged residents to be on high alert.