"This is clearly a very distressing time for Leeann's partner and family, her siblings and parents. They have been very patient, but as time moves on they are becoming more and more anxious," Detective Sergeant Beatson added.
"They haven't given up on her though, and continue to remain optimistic. They have continued to look for her, distribute flyers calling for help, and are actively speaking to people themselves."
Ms Scott's brother Manuel Scott, who lives in Auckland, said her family would not give up hope, and were determined to do what they could to bring her home.
"We all hope for the best but are prepared for the worst," he said.
Meanwhile her elderly mother, Irene Basham, who lives at Cooper's Beach, has made another impassioned plea for information.
"If anyone knows where Leeann is, or has any information that can help the police find her, please call them, call the police, so we can get our girl home," she said.
Detective Sergeant Beatson said police were keenly interested in any sightings of Ms Scott on or since the day of her disappearance.
"Any scrap of information we receive may help piece together the puzzle of what has happened and where she is," he said.
When last seen she was wearing a bright orange Northface Summit hooded rain jacket, black exercise-style pants and a pair of creamy/brown Nike walking shoes. She may have been walking along SH10 at Cable Bay immediately before she disappeared on the morning of Friday December 12.
Anyone who has any information is urged to contact the Kaitaia police on (09) 408-6500, or, if they wish to provide information anonymously, Crimestoppers on 0800 555-111
