If I am currently on unemployment can I still apply for SS benefits since I'm 62 yrs. old in Kentucky?

Yes you certainly can get both. If you return to work, you must notify Social Security if you make above a certain amount (currently $14,160, but changes yearly), since that will reduce the amount of Social Security benefits you get. There is a credit, however, once you hit full your full retirement age (which is 66 for you) for any month you did not receive a full check. Remember, though, for unemployment, you do have to state you are looking for work.