A Melbourne mother, accused of attempting to murder her three children by driving the family car into a creek, allegedly searched online for "how to kill a child quickly," a court has heard. The woman, in her 30s and who cannot be named for legal reasons, faces multiple charges of attempted murder for the incident involving her children, all aged 12 and under.

The Melbourne Magistrates' Court heard details of the woman's deteriorating mental health and her alleged online search history as she fought to be released on bail. The court was informed that the woman, who suffers from severe obsessive-compulsive disorder, allegedly attempted to harm her children just three weeks after the birth of her third child.

According to reports, the woman's mental health declined, leading her to reportedly lock herself in her bedroom while her husband cared for the children. When he left the home briefly to go shopping, the woman allegedly instructed her eldest child to go to the bathroom, where she then attempted to drown him in the baby bath. The boy reportedly asked his mother, "Why are you doing this?"

Investigators were told the boy stated he "held on" and used his legs to prevent himself from being submerged. Following the alleged bathroom incident, the woman reportedly suggested they go for a drive. Upon arriving at a creek with a boat ramp, the boy told police he feared his mother would drive them into the water.

"I thought nah… but she did," the child recounted, describing how his mother allegedly locked the car doors and accelerated towards the water at "full speed." Detective Senior Constable Amy Tuck testified that the woman allegedly told the primary school-aged children to "get out" as water began to fill the car, before she reportedly pushed one of the children underwater. The child later told police, "She said she was trying to save me … but it felt like I was giving her a piggyback."

Nearby witnesses, alerted by screams, called emergency services and entered the water to rescue the children. When questioned by police at the scene, the woman allegedly claimed it was an "accident" and that she had "just slipped."

An analysis of the woman's phone revealed a series of concerning searches in the period leading up to the alleged incident, including "how to kill a child quickly," "why do I feel suffocated at home," "how do you know if you're cut out to be a mother," "difference between manslaughter and murder," and "murder sentence Victoria." She is also alleged to have sent text messages to her mother expressing sentiments such as "I want to walk out mum," "I can't do this anymore," and "I want to put the baby up for adoption."

Detective Senior Constable Tuck stated that the woman's life had been impacted by "obsessional thoughts" and that she had been prescribed medication by a perinatal psychologist. The court was informed that the woman's symptoms have reportedly improved since receiving treatment in prison following the alleged incident.

Magistrate James Henderson is expected to deliver his decision on the bail application on Wednesday. If granted, the woman is understood to be planning to reside with her parents. She is scheduled to appear in the Supreme Court for a directions hearing on October 12.