A man was walking his Dalmation in an alleyway off Waterloo Road when the XL Bully attacked him and his pet.
Officers say the man and both dogs were hurt.
A 46-year-old man was arrested on suspicion of being in charge of a dog dangerously out of control and released on police bail.
Last week, a man died in Wigan after being savaged by a dog – reported to be an XL Bully – which was dangerously out of control
Police are appealing for anyone who witnessed the Brighouse incident – which happened at around 7pm on Sunday, March 5, to get in touch.
Information can be passed on by calling police on 101, quoting crime reference 13230133960, or by using the live chat facility on West Yorkshire Police’s website.
Alternatively, witnesses can call the independent crime-fighting charity Crimestoppers on 0800 555111.
