The incident happened on Saturday as a 48-year-old woman walked her dog on a leash in Moat Park.
At around 7:45pm another dog with a black coat approached and appeared to be on its own. The animals started to fight prompting the male owner of the other dog to run over.
He then started to kick the woman’s dog a number of times and acted in aggressive manner towards her.
Officers are keen to trace the man in connection with this incident and are appealing for the assistance of the public.
He is described as around 6ft tall, medium build and wearing a dark coloured woolly hat.
PC Calum Wilson said: “This was a traumatic experience for the victim to go through and we are very keen to hear from anyone who can help identify this man.
“Those with information can contact police on 101 or, alternatively Crimestoppers on 0800 555 111.”