I don't see the difference between this and finger printing.
The state has no right to force me to subject my body to any medical procedure, however trivial, and no right to any part of my living flesh. None. At all. Not a microgram.
If they have actual probable cause to believe I may be involved in the commission of a specific crime for which they have DNA evidence, they can (with a warrant) search my home for hair and skin flakes. Or if they have enough evidence for an arrest they can lock me up in a clean room for the night and take my sheddings. So it's not even the case that this gives them critical evidence they can't get any other way -- it's all about the convenience of the police and the assertion of state authority over the bodies of citizens.
I'm not a Christian, but I always liked Jesus's line "Render unto Caesar the things that are Caesar's, and unto God the things that are God's." My living flesh -- that matter whose dance is *I* -- is not Caesar's. It is the most divine thing I know, and I will not surrender it to the state willingly. Should the matter ever arise, they will have to take it from me by violence. I reserve the right to defend myself against such an assault, though I also reserve the right to decide that resistance is tactically unwise.