The NY Times editorial board believes it's a good idea to allow law enforcement to search and investigate partial DNA matches. The cite a recent example in CA in which a serial killer was charged after being found through a partial DNA match to his son.
I do not think that it is a good idea, nor constitutional, for someone to be investigated simply because they have a family member committing crimes. If the police are unable to find the criminals then maybe we need better police, but what we do not need is for police to interrogate and bully innocent citizens. I wonder how that pillar of liberty, the ACLU, will react to this.