What screening tests are done at birth depends on what state you live in. I don't know why the same testing isn't mandatory throughout the US.
Some types of muscular dystrophy are included in the newborn screening in some states, such as genetic spinal muscular atrophy. However, that still leaves a lot of types that aren't tested for initially.
Some types of MD are apparent very early on: the baby doesn't start holding his head up when he should, his muscle tone is very "floppy," he doesn't grab and hold your fingers, etc.
In other types of MD, the milestones are all reached on