Ms Turei's husband, Worik Stanton, of Waitati, said he feared Timmy had injured himself in his escape and crawled away to die.
He might also have been picked up by someone.
''I'm extremely worried; I think the prognosis is not good.''
It was thought Timmy jumped a fence, or he might have tunnelled out.
''Dogs can get through incredibly small gaps,'' he said.
Mr Stanton can be contacted on 482-1804.