The 2010 long form census asks about citizenship in question 13.
https://www.census.gov/dmd/www/pdf/d-61b.pdf
It also asks many other questions which are far more trivial but personal.
Long form Question 17 asks if the person can dress or bathe themselves. - won’t that cause an undercount?
The Census 2010 Didn’t Use a Long Form
Fastforward to the Census 2010. The decennial Census 2010 only collected basic demographic information (just like the Census 2000 Short Form). The Census Bureau did not include a Long Form Questionnaire in the 2010 Census. Here’s a copy of the 2010 Census Form. You can see that the Census 2010 Form is much more like the Census 2000 Short Form than like the Census 2000 Long Form. In fact, the Census 2010 Form is one of the shortest Census forms in history.