Your relatives' DNA may implicate you.

The privacy community has been concerned for some time about the ethical, legal, and practical issues surrounding DNA testing and the fact that you share a lot of your DNA with relatives. Much of the concern had been for things like insurance: Should the fact that I carry a gene predisposing me to blood clots affect my sister's insurance rates, even though she has not been tested for that gene?

The Washington Post has a very interesting story by Ellen Nakashima that details an actual criminal case where a man was arrested for murder based on DNA testing of a 5 year old Pap smear specimen from his daughter. While it appears that justice was done in this case, the Fourth Amendment implications of this type of search are not so clear. The article discusses a number of them in depth.