A man - who was with his family - made homophobic comments to a passer-by after the victim's dog approached him.
The incident happened at about 6.15pm on Saturday, April 22, at Upton Country Park when the owner ran over to retrieve his dog.
At that point the man is alleged to have made the derogatory comments, a police spokeswoman said.
The offender was described as black, around 5ft 8 inches tall and of muscular build. He was bald and was wearing a black t-shirt and grey tracksuit bottoms.
Anyone with information can contact Northamptonshire Police on 101. Alternatively, they can call the independent charity Crimestoppers anonymously on 0800 555 111.