STAR credit in New York. Is there any way to check and see if I received a STAR credit in 2017? While I've received one in years past I don't recall getting one in 2017?

The question is asking if you got a STAR check in 2017, which you should probably remember.

For homes bought before 2016, the STAR is a reduction of your property tax bill applied by the tax receiver in your town or county.  You simply pay less tax, you don't get a money rebate.

For homes bought after 2016, you pay the full property tax bill and then get the STAR as a check from the state.  If you did get the STAR check, you need to reduce your property tax deduction in the federal part of the program by the amount of the rebate you received, in addition to answering the question in the state form.