They don’t need your DNA to connect you to solve a cold case. They determine we shares tiny chunks of DNA with a sample from a crime. With that, they find the family tree of the known person and can often determine who the guilty party is.

As in they know the suspect shares a paternal great grandfather with this person and a maternal great great grandmother with that person so we know it’s one of these people. Then the police collect trash to find who from the limited pool the crime DNA belongs to.