Detectives are looking for an offender with a penchant for fashion after a man, who had threatened a couple with a tomahawk in East Victoria Park, dropped his fedora as he ran away.

WA Police spokeswoman Susan Usher said a man and woman, both 27, were walking along Somerset Street near Aqualife between 5.30pm and 6pm when a man on a mountain bike rode up behind them.

Tomahawk-wielding offender was wearing a beige fedora.

Ms Usher said the offender, armed with a tomahawk, got off the bike and threatened the couple before demanding the woman give him her handbag.

She refused and the couple ran towards Shepparton Road with the man following them.