Inspector Graham Hawcroft, of West Yorkshire Police, said officers attended a property on Cross Flatts Row in Beeston at around 2.30am.
During the operation the people who were in the home, understood to be one man and two women, went to a different property which was also subsequently searched.
Insp Hawcroft said: "We were looking for a male who is wanted in connection with a firearms offence."
He added: "It was an armed operation."
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The person officers were looking for was not found, he said.