Open Question: Am i eligble for unemployment pay?

Today i was told that I will be laid off. I have been with my job for almost five years, live in kentucky. I was however, offered to take a different position with the same pay, or another for more pay. However, both schedules are completely different from my current and would conflict with child care. If i decide not to take either of those positions will i be ineligible for Unemployment? Someone said that if i decline, then Unemployment would deny me benefits.