Last time I switched employers I just needed a record of my previous health check- if you can make a photocopy of it that might even work. Of course, my previous employer kept the health check report and I guess immediately chucked it when I left so I needed to get it redone even though it had been less than a year. They say the chest x-ray radiation only harms your body for three months....
Like xwarrior said, it's really just going to depend on what your new employer says.