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The National Shooters Association said Mrs Collins had broken the law because was not licensed to the use the weapon and had shot a pistol outside of a gun club.
A picture of the minister firing the gun at an ESR testing facility last month was placed on her Facebook page.
Association spokesman Richard Lincoln complained to Police Minister Anne Tolley, who referred the matter to police.
When police said they would not intervene because Mrs Collins had been supervised at the time, Mr Lincoln wrote a letter to the Independent Police Conduct Authority.
He said he had laid the complaint because he wanted "one law for all".
"We, as civilian gun owners, don't want to have these laws imposed on us with what appears to be politicians taking liberties and exemptions that they're not entitled to."
Mr Lincoln said he was not ruling out a private prosecution.
Mrs Collins said she could not comment on the complaint while it was before the IPCA.
But Prime Minister John Key dismissed the complaint as "ridiculous" and "OTT [over the top]".
"I wasn't there and I don't know all the elements of it but I've seen the correspondence with police. She was at ESR, the police were comfortable that she would have been under supervision.
"In the end, when ministers go into those environments it's not at all unusual that we're asked to test things, try products.
Mr Key, who was speaking after attending an event at Tawa College, said: "I've just had some cordial, someone's given me some jam. I know that's not quite the same as a gun but she wasn't walking down the street with it, she was in a highly controlled environment."
He was also asked about Mrs Collins' ownership of a taser, which usually required a special licence.
"You'd have to ask her. She's never used it on me, so I'm not aware of her having one."
Mrs Collins, a former Police Minister, said the taser was non-operational and was stored in a perspex box.
She said it could not be charged up, "although it would be tempting occasionally to be able to".
- By Isaac Davison of the NZ Herald