Principals say information from the Census have financial implications for schools.
The Ministry of Education will use the information next year to recalculate the decile rating that indicates which schools have the most children from economically disadvantaged areas.
Principals of low-decile schools say they do not want their rating to rise because they will lose funding.
But they also say a drop in the rating can also be a problem, because parents sometimes mistake it for an indicator of quality.
Any changes to the decile system resulting from this year's Census will take effect in 2015.