Police and Child, Youth and Family investigated a relationship between a man in his 50s and a 16-year-old girl last year.

However, no further action was taken as police found no sufficient evidence for further investigation.

The man and the teenager, who turned 16 last August, had known each other for three or four years, Fairfax Media reported.

It reported the pair would often meet and talk on the netball courts in a Lower North Island town, where the girl's family lived.

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The father of the girl told Fairfax the man was his friend and had moved into their home to stay in December 2015.

Last year the investigation into the relationship began after complaints by family members, before the teen willingly left home with the man, the father told Fairfax.

The father said the man told him, "I wouldn't do anything of the sort, I'm religious".

The man was asked by Fairfax if he had groomed the girl, but said he had to leave, while the teen decided to leave for her safety.

"I was moving up north, and I had a conversation with her and she said 'can I come?', and I said 'that's totally up to you'," the man said.

However, the teen's father called for law changes to allow police "to have more power to act in these situations".

The man said the 16-year-old argued with her dad, and told her father if the man ever left she would too.

The man told Fairfax the girl would remain a virgin until the pair married, and would not force a sexual relationship.

The man said the teen told him about October last year she loved him and would like to marry when she turned 18.

"I think it was in December last year, I realised, 'I love this girl', but it's only because of her family situation that she is with me," he said.

A police spokesperson said police received a report of concern last year and an investigation occurred.

"We are not able to comment on the specifics of this case due to the rights to privacy of the young person involved."

However, the spokesperson said it is a criminal offence for a person to engage in a sexual relationship with any other person under 16 years of age.

"Police take any such allegations seriously."

The spokesperson said for police to commence any criminal prosecution there must be sufficient admissible evidence which is likely to lead to a successful prosecution.

"If the underage person declines/refuses to speak to police or fails to disclose that a sexual relationship had occurred it is often difficult for police to meet that threshold of evidential sufficiency.

"Each case must be assessed on its own merits. Police may speak to any alleged offender advising them of the law, even though a formal complaint has not been received."

The spokesperson said police will share information with CYF to assist with the welfare needs of the teen involved.

A CYF spokesperson said concerns were raised about a man "having an inappropriate relationship with a [then] 15-year-old girl".

"We spoke to all the parties involved, including the young woman alone, all parties were adamant that there was no basis to the concerns."