What is collected and stored is a small blood-spot sample from a heel prick on a newborn. This is used to test for various kinds of conditions that affect newborns.
This isn't a full DNA genome sequence or even any data at all, just the blood-spot specimen.
Law enforcement does not have automatic access to this sample, but individual samples have been given to law enforcement through court orders or warrants. There isn't a clear SOP for how law enforcement typically gets this information or how often it's given to law enforcement, but there's been proposed legislation to make this more transparent.