We wouldn't be able to check-raise in position, so I think you mean check back the flop if our opponent checks to us?
Usually if we were the ones to 4-bet, we would be c-betting the flop. If our opponent 4-bet, more often we would check. But it comes down to a lot of factors like how well we've connected, flop texture, opponent tendencies, and how big the pot is relative to the effective stack.