well I didnt know that. In having a quick google to find the answer to this I am amazed to find that before man arrived there were only two species of mammal in NZ and those were bates. Europeans introduced a lot of species- all the farm animals, deer, stoats, rabbits, hares. Even wallabys from Oz. I get the impression squirrels are specifically banned from being brought into NZ. I shall have to read up on this! Interesting subject.
I thought it might be because squirrels were not good for hunting like rabbits & deer so there was no need to introduce them. But I also thought they would maybe have boarded ships like rats & got to NZ that way? The climate here would suit them so they wouldn't have died out surely?
Apart from raiding back-garden feeding tables, squirrels haven't developed a relationship with man (i.e., scavenging for food and invading our homes) in the same way that rats have. American grey squirrels were introduced deliberately to the UK in the late 1800s, but I don't know why.
No squirrels in Oz as well, no mice, rats, foxes or rabbits either until 'colonisation' - I think 'Australasia's' native animals developed along different lines from those of Europe and the Americas - we seem to have an abundance of unusual mammals capable of existing with dry conditions, etc.