Yes. Indiana will most assuredly want to tax your rental income that has its source in Indiana.
You should be filing Form IT-40PNR which is for use by part-year residents and non-residents. Since you say you are being asked about a county of residence, I suspect you are preparing a resident tax return.
Please go back to your personal information and be sure that you indicated that you need to file an Indiana state return, and that you have indicated within TurboTax that you are a non-resident of Indiana.
