"It was pouring with rain, one police officer was shining his torch and the other was sort of sitting behind me holding my hand and telling to me to stay calm and to breathe.
"My husband was attending to things in the nether regions ... Three more contractions and the baby pops out."
The Te Kuiti couple's daughter Ariana Lee Smith, weighing 3.4kg, was born shortly before midnight, less than an hour after her 33-year-old mother went into labour.
"We were intensely delighted as you could imagine," Mrs Smith said.
"The policemen were pretty happy too. They were saying, 'Oh you must be so proud'."
Mrs Smith was taken to hospital by ambulance a few minutes later and said she never got a chance to thank the officers who helped her and her husband.
One drove the couple's car to the hospital and the other escorted them there while Mr Smith sat in the ambulance.
Said Mrs Smith: "These guys were great and we really would like to say 'thank you' to them."