On the IL state return, it asks "Did you own your 2016 principal residence" for the property tax credit. How do I answer if i owned it for only part of the year?

[TomD8]

Answer Yes.  If you bought a house during the previous tax year, you may use the property tax on that house to figure your credit - providing you figure only that portion of your taxes that pertains to the time you owned and lived at the property during the tax year. For example, if you purchased and began living in a house in October 2016, you may
use an amount equal to three months of your total 2016 property tax to figure your 2017 property tax credit.

You may not use the property tax paid on a house you bought in 2017 on your 2017 return. The seller was liable for the tax and will take the property tax credit.

http://www.revenue.state.il.us/Publications/Pubs/Pub-108.pdf