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It is also understood the incident was alcohol-related.
Police have investigated but are not laying any charges.
"Police conducted an investigation after receiving a report of an individual sending an unsolicited image," said a spokesperson. "The investigation determined it did not meet the threshold for prosecution. As such, no further action will be taken."
Falloon, a first-term MP in the Rangitata seat, quit politics today and said he had made a "number of mistakes".
In his statement, the 37-year-old said: "As I noted in my maiden speech three years ago, when I was younger I lost three close friends to suicide," he said in a statement.
"It was an extremely difficult period in my life. Unfortunately, recently, another friend took their own life, which has brought back much unresolved grief.
"I have made a number of mistakes and I apologise to those who have been affected.
"Recent events have compounded that situation and reminded me of the need to maintain my own health and wellbeing. I have again been receiving counselling.
Ardern said today the matter was for the National Party to deal with and they had dealt with it appropriately by asking for permission to forward the information and by keeping it confidential.
Falloon, the MP for Rangitata, issued a statement this afternoon saying he will not contest September's election, citing concern for his "own health and wellbeing".
"I apologise for this disruption to my colleagues and to those I serve in mid- and south Canterbury."
He thanked Collins for her support.
Collins said in her statement Falloon was facing "significant mental health issues".
Sending harmful content is one of Collin's zero tolerance issues.
As Minister of Justice, Collins put up the Harmful Digital Communications legislation which primarily targeted cyber-bullying, and covered the sending of objectionable material.
Collins said "the National Party was advised of an issue relating to Andrew late on Friday afternoon and we have dealt with it this morning".
"Andrew is suffering from significant mental health issues and his privacy, and that of his family, must be respected."
Falloon becomes the third MP to quit after Collins was appointed leader last week.
Senior MPs Nikki Kaye and Amy Adams have decided to quit politics, but said Collins' promotion to the leadership was not a factor in their decisions.
Falloon, a first-term MP, said that he told Collins today that he would not contest the September election.
Where to get help:
• Lifeline: 0800 543 354 (available 24/7)
• Suicide Crisis Helpline: 0508 828 865 (0508 TAUTOKO) (available 24/7)
• Youth services: (06) 3555 906
• Youthline: 0800 376 633
• Kidsline: 0800 543 754 (available 24/7)
• Whatsup: 0800 942 8787 (1pm to 11pm)
• Depression helpline: 0800 111 757 (available 24/7)
• Rainbow Youth: (09) 376 4155
• CASPER Suicide Prevention
If it is an emergency and you feel like you or someone else is at risk, call 111.