The NZ Council of Christian Social Services collects a large amount of data and uses it to criticize the government.
What happens to people declined support? A total of 35,128 applications for ‘working age benefits’ were declined for the period July 2013 to September 2014. Collectively, this represents a comparatively large number of people who walked away from a Work and Income Office without the support they requested.
This data isn't routinely published but I have some comparative figures from my own OIA requests. Note the NZCCS data is for 14.5 months - mine is for 12 months.
Under a Labour government the number of sole parents declined a benefit was higher.