Armed officers descended on a street in Osmondthorpe after worried residents told police they had seen a man with a gun.
The incident took place outside a house on Rookwood Road, Osmondthorpe, on Tuesday afternoon.
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West Yorkshire Police said:
"At 4.45pm on Tuesday police received a report of a man with what appeared to be a handgun making threats outside an address in Rookwood Road, Osmondthorpe, following an earlier altercation.
"Armed officers were sent to the scene and a 38-year-old man was arrested from a nearby address on suspicion of possession of a firearm with intent to cause fear of violence.
"A gas=powered BB gun was recovered during a subsequent search of the property.
"The arrested man was later released on bail with conditions pending further enquiries."