Melbourne Magistrates' Court has heard Ashley James Rei-Paku was involved in a crime spree in October and November last year, during which he allegedly stole cars, fired gunshots at police on two separate occasions and struck a man in the chest with the blunt side of a small axe.

In the early hours of November 19 last year, Mr Rei-Paku allegedly struck the man with the axe after attempting to steal a car from outside the man's Caroline Springs home. Also that morning, he is accused of firing a shot that hit a police vehicle during a short pursuit in Werribee.

About 6pm that day, the court heard, he was in a utility in the Werribee Plaza car park when heavily armed special operations group officers confronted him.

Mr Rei-Paku reversed away from police and into the back of a family's car, prosecutor John Livitsanos​ said, and was reaching for a rifle when police tasered him and arrested him soon afterwards.

Mr Rei-Paku, 24, on Tuesday pleaded not guilty to more than 50 charges, including reckless conduct endangering death, assaulting an emergency worker, assault and theft, weapons and drugs offences. Magistrate Luisa​ Bazzani committed him to stand trial after a day-long committal hearing.

A woman told the court she and her husband were at the back of their car setting up their baby's pram when they saw the utility reverse and crush the pram and crash into the back of their car.

The woman said her son, who was two months old at the time, was still in their car and that she leapt inside to take him from his seat and into her lap.

"I was just looking for my baby, [concerned] 'Is he all right?' I was so worried," she said.

"It was [very] frightening. We were there for shopping. We never thought something like this would happen there."

The court heard that on the day before his arrest, Mr Rei-Paku fired a rifle at an off-duty policeman, who had followed the accused man's girlfriend to a house after she was seen driving erratically.

The policeman told the court he pulled up and asked the woman what she was doing, but that she ignored him and walked towards the house. Moments later he saw a man in his mirror and heard him yell 'you're f...ed'. When he saw the man unwrap something from a blue towel or blanket, he drove away.

"I just had a feeling something bad was going to happen so I wanted to get out of there," the policeman said.

As he drove he heard a crack and later found a bullet hole in his car, in line with where his son's child seat was. The child was not in the car at the time.

The mother and off-duty policeman cannot be named.

Mr Rei-Paku was remanded in custody to appear before the County Court on Wednesday for a directions hearing.