It allegedly happened during a protest on St George's Square on 1st March.
Police are appealing for witnesses as investigations continue into a hate crime incident in Hebden Bridge.
Halifax Police would like to speak to anyone who witnessed or had information about the incident which took place at about 1.30pm on St. George's Square on Friday 1st March during a protest.
It occurred during a verbal exchange between a man and a female protestor.
The incident was reported to the police and officers have recorded a hate crime in connection with words allegedly spoken by the male.
Anyone who was present at the time and who witnessed the incident is asked to contact PC 1823 Jack Curbishley on 101 referencing crime number 13190119804.
Information can also be given online at 101 Livechat at www.westyorkshire.police.uk/101livechat or anonymously to the independent Crimestoppers charity on 0800 555 111.