Her stepfather, Paul Nicholson, was discharged after a brief hospital stay.
Wellington-born Ms Tamaki was still in a critical condition yesterday in an induced coma in Bellevue Hospital.
She had bought the helicopter sightseeing tour as a present for her partner's 40th birthday.
"The Tamaki and Nicholson families have had a close relationship for many years and both families are here supporting each other through this difficult time," the Tamakis said.
Ms Marra's stepfather and sisters Amanda Moore and Annie Nicholson said in a separate statement: "Sonia was loving her first experience in New York, the city and its people.
"She was incredibly happy to be here and it gives us some comfort to remember that. We are a strong family and will cope with our loss in our own way."
The family thanked those involved in the rescue "who acted with great courage", and hospital staff and New York police "for their compassion, kindness and care".
They said pilot Paul Dudley, a family friend, also "acted with great bravery in the rescue".
The National Transportation Safety Board said it was looking into the winds at the time of the crash and weight allowances for the aircraft. It said it had not found any rupture of the helicopter's engine or indication of fire.