For a deceased relative 2016: don't have to pay federal tax but owe state tax. What to do?

Hi: a deceased relative I am the executor for died in early 2016.  I had the CPA handle the enormous1041 form, but I handled the 2015 normal tax form for my relative and now am investigating if I must file anything for the relative's 2016 income (exclusively $10,000 total from stock dividends and refunds from overpayment of 2015 taxes).   Per the IRS's Tax Assistant page I don't even have to file a federal return for my relative (see  https://www.irs.gov/uac/do-i-need-to-file-a-tax-return  )  However, when I plug the numbers into 2016 turbotax, although the FED tax due is ZERO, the STATE tax due is $68.  What should I file?  Thanks much.  I did search the questions in the software and on your website before posting, so I hope the question is a good one!

CW
Boston