The mum and her seven-year-old daughter were walking through Tirhatuan Park in Dandenong North on March 25 when a man on a dirt bike allegedly skidded to a stop near them about 6.30pm.
The pair were allegedly forced to run towards some nearby basketball courts on Kriegel Way, where the man followed them and began doing laps around the basketball courts and nearby tennis courts.
Police allege he then took off his helmet and pointed a black handgun at the pair for about 10 seconds, before riding away in a south-easterly direction towards Stud Road.
A computer-generated image of the man they believe may be able assist with their enquiries, along with the motorbike gear he was wearing at the time has been released to the public.