I remember playing a game very like the one you describe. In our version whoever was IT had to catch and touch the top of another persons head for them to be IT too. This went on until the playground was full of ITs and only one quarry was left to catch. We called the game "TEE-ACK" but I've no idea of it's origins, nor do I remember a song. I do remember all the children chanting "TEE-ACK,TEE-ACK," as they chased their target and I recall that the game could get quite rough at times.