The man posted a picture on Facebook of a Statistics New Zealand letter with a note saying they will "pursue prosecution" if the person doesn't fill out the compulsory survey.
However, it seems to be an empty threat - Statistics New Zealand has not prosecuted anyone in the past 15 years for a non-Census survey.
The statement from Stats NZ said:
"Stats NZ would like to thank a Hamilton family for completing a Labour Market survey form today, (Friday) after they complained on social media," a spokesperson said.
"Stats NZ apologises for a note left for the Hamilton household on Thursday night, which incorrectly threatened prosecution if the Household Labour Force Survey was not completed.
"The family has been in contact with Stats NZ this morning (Friday) and they willingly completed the survey.
"We are glad they took the time to help complete the survey, which is vital to provide regional and national figures on jobs and unemployment," Stats NZ general manager, Collections Operations, Ray Freeman said.
The note, posted below, said, "This is a compulsory [government] survey."
"I am the local area leader for Stats NZ and we will persue [sic] prosecution if you fail to comply. We are somewhat dismayed at you [sic] refusly [sic] to talk to our interviewer.
"Please call me on the below number urgently."
Statistics New Zealand do have the power to prosecute non-compliance under the Statistics Act 1975, but has not prosecuted anyone in the past 15 years for any incompleted surveys outside of the Census.
The printed text on the card says: "Sorry I missed you today. You have been selected to participate in a Statistics New Zealand survey. Sorry I missed you when I called today."
The man who posted the picture did not want to be named. His Facebook post said his partner answered the door but was too busy to take part in the survey at the time.
"I appreciate they've got a job to do but threatening legal action seems a bit of an extreme way to go!" it said.
Statistics New Zealand said a senior manager was looking into the note this morning but has not yet confirmed, or denied, whether the author was its employee.
Forty-six people were convicted for not filling out the 2013 Census, and 37 were fined.