Thomas Hughes, 56, faced Melbourne Magistrates Court on Thursday, four days after two people were taken to hospital from Ascot Vale with non-life-threatening stab wounds.
Hughes has significant health issues and made no application for bail, his lawyer Anthony Brand said.
"He was discharged after a serious car accident ... suffering from broken ribs," he said.
"He has probably got some mental health issues that need addressing fairly urgently, particularly in view of matters arising from both the incidents involved and the subsequent accident."
Mr Brand asked that Hughes receive a comprehensive medical assessment in custody.
Police believe the victims, a 46-year-old Moonee Ponds man and a 60-year-old Ascot Vale woman, were known to Hughes.
Hughes was allegedly stopped by police in Kensington before fleeing and crashing a car into a tree down the road.
He is charged with false imprisonment, intentionally causing injury, reckless conduct endangering serious injury, assault with a weapon, making threats to kill and failing to stop when requested by police.
He's due to return to court on August 25.
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