Well, not tissue, but DNA. A new UK law in the soon to go into effect would make it illegal to test someone's DNA without their permission.
The idea is being floated because, apparently, politicians are afraid that, after leaving their DNA all over the place, someone will pick it up and tell the world that he or she is prone to high blood pressure. Something like that.
In practice, it could keep employers and insurance companies from discriminating against someone based on undiscovered genetic conditions. Certainly not a bad thing. Still, I place it in the category of "strange, but most likely necessary in about 10-15 years."