Confusion on KY local income tax

Hi, I work from home in Kentucky and my job is located in Ohio. The two states have tax reciprocity. I notice there wasn’t any local income tax taken out of my paycheck, shouldn’t there be? My husband works in Kentucky and it was taken out of his paycheck. Also, do I need to report local income tax for Kentucky on my taxes? If so how do I do this as I don’t see anything on the Kentucky website and didn’t receive anything in the mail.