Queenstown Lakes District Council parks manager Gordon Bailey said the council was investigating the removal of the trees - one of which was chopped down yesterday at Kelvin Heights.
The mature weeping willow, on Willow Pl at Kelvin Heights, was estimated to be about 50 years old.
"In the course of clearing power lines, Delta had received a suggestion from a resident to remove a weeping willow."
Unbeknown to Delta, the council had previously received two applications to remove the tree - both of which had been turned down, primarily because the tree was in good health "and because you would expect to find willows in Willow Pl", he said.
Although Delta immediately offered to replant another tree, Mr Bailey said the matter needed to be referred to Lakes Environmental, the council's regulatory organisation.
"This is the second tree we have passed on for investigation, the other being a tree cut down in Devon Pl in Arrowtown.
"These are trees belonging to the community, for the community on community land," Mr Bailey said.
A great deal of time and money was invested in caring for trees because of the immense amenity value they brought to the district.
"In an environment such as ours, trees are essential. That's why we have a tree policy and that's why you cannot simply cut down a tree without first asking what the rules are," Mr Bailey said.