Which statement is true about the law of conservation of energy for an object released from a certain height above the ground

The question is really specific enough, but I will take a guess. If nothing else changes (like the mass or the gravitational constant) then the Potential Energy will increase with an increase in height. Ep will decrease with a decrease in height.

If you are talking about Ke, then the height does not matter unless the object is moving up. Then it slows down. When that happens the Ke decreases because the formula for Ke = 1/2 m v^2. If v becomes less then Ke becomes less.

I suppose you could say if the object is going down and the distance is decreasing then the speed will increase. It's an inverse relationship.

I think you are best talking about Pe.