An HNZ executive team agreed last November any tenant who kept a dog without permission after being warned could be issued with a 90-day eviction notice.
A tenant would need written permission from HNZ to keep a puppy of a permitted dog.
If a puppy was kept without permission, a "notice to remedy" would be issued to remove the animal, a document said.
HNZ tenant Chanel Brogan, of Wakari in Dunedin, said she was "gutted" when HNZ declined her request to get a dog last week.
She had planned to rescue a dog destined to be put down.
"I'm a grown adult - I feel discriminated against," she said.
HNZ tenant Lara Elliott, of Dunedin's Andersons Bay, said she rescued her dog Mischief as a puppy while living in private rental accommodation.
Mischief was registered and microchipped and Ms Elliott got permission seven months ago from HNZ for the dog to move with her into a state house.
Stopping her from having a dog would be "devastating", as she had muscular dystrophy and a dog was comforting for her.
"If I had to give up my dog, I'd be heartbroken. They are a part of you."
The HNZ documents said a dog could be kept if it assisted a person with a disability or was "important to therapy for a mental illness or other chronic health condition".
The document revealed HNZ deemed some dogs a "health and safety risk".
Between July 2011 and June 2012 there were 37 "dog-related incidents", including one leaving a HNZ staff member and four contractors requiring medical treatment.
HNZ lower South Island manager Kate Milton said tenants were discouraged from owning dogs.
"Dogs can cause damage to our properties, they can be a nuisance to neighbours and they can make it difficult for our tenancy managers or contractors to visit our properties."
Many state houses were unsuitable for dogs, she said.
Although dogs played an important part in the lives of many tenants, it was not an easy rule to enforce. HNZ's "first principle" was not to allow dogs, she said.
"We ask that our tenants respect this approach."
Dunedin Dog Rescue manager Michelle Hagar said it was "disheartening" an HNZ tenant could be refused dog ownership.
A petition had been started asking HNZ to change its dog policy to allow tenants to own registered, microchipped and desexed dogs.
The petition had been organised to ask the Government for the policy change, she said.
A dog is welcome in a state house if:
* It has been trained to assist a person with a disability
* It is important to a tenant's therapy for a mental illness or other chronic health conditions
* It has been at a property for many years and has been present at inspections
* Decision to grant permission made on a case-by-case basis
