The incident happened in the early hours of Saturday, March 30 in George Street, Liversedge after officers had previously searched another property on St Stephen's Road, Lockwood.
A spokesman for West Yorkshire Police said: "Armed officers were deployed to an address in St Stephen’s Road in Lockwood at about 11.30pm on Friday March 29 after police received a report of a male making threats to use a firearm."
"The address was found to be empty.
"Following further enquiries the officers attended an address in George Street, Liversedge at about 1.20am and arrested a male on suspicion of making threats to kill."
No weapons have been found and enquiries are continuing.