Christopher Hennigan, 34, of East View, Cross Gates, has been charged with possession of a firearm with intent to cause fear of violence in relation to the incident at an address in Elmet Way, Swarcliffe, on Sunday, June 12.
He is due to appear at Leeds Magistrates Court this morning, police said.
He was arrested at an address in Little Smeaton, North Yorkshire, on Monday.
A 32-year-old woman who was arrested at the time on suspicion of assisting an offender has been released under investigation.
A 31-year-old woman who was arrested on Monday in relation to the firearms discharge has been released on bail pending further enquiries.