Your DNA and fingerprints are literally everywhere you go, and they don't decay as soon as you leave. Hell, even passing close by a person can transfer your DNA to their clothes.

If the cops have a DNA Database, they "just" need to collect all DNA from a crime scene to compile a list of suspects, and by doing so, they're flipping the question of guilt around, you're no longer innocent until proven guilty, but guilty until proven innocent. You now have to prove you didn't "do it".