"That wouldn't draw attention running," they sarcastically tweeted.
However, the tweet-a-thon quickly became a victim of its own popularity, with a search of the hashtag #poltwt bringing up hundreds of spam tweets.
Most were from the accounts of an apparent legion of scantily clad women wanting to push messages entirely unrelated to law and order.
TrishGCrazierop, whose profile picture was of a woman in a bikini in front of a surfboard, asked those searching #poltwt whether they had heard of a particular debt consolidation website.
@BekyztF398, whose profile picture featured a topless woman, posted a link and said "I find myself investing more time about sex websites recently? Is something wrong with me?"
According to an official NZ Police Twitter account, @betterworkstory, #poltwt would provide a "fascinating insight into daily policing".