Police were called to Alpine Close shortly before 1pm today after it was reported that an armed man had made threats and then fled the scene.
It led to armed response officers stopping a vehicle in the Soothill area of the town and making two arrests.
No handgun has been recovered but officers did find what was described as a Taser-type device.
A West Yorkshire Police spokesman said: "Police were called to Alpine Close in Batley shortly before 1pm today following a report that a man with a handgun was making threats before making off in a vehicle.
"Officers were deployed and stopped a vehicle on Highfield Court. A man and woman were arrested in connection with the incident.
"The vehicle, and a Taser-type-device have both been recovered."
The spokesman said enquiries into the incident were ongoing.