Ok, so DNA left at the scene of a crime is indeed evidence. But..you've got to tie the DNA to the suspect.
In order to do that the suspect must supply a DNA sample, either willingly or forced. What if he refuses? Can he not refuse under the Fifth Amendment?
Providing DNA is tantamount to testifying against oneself, in my opinion.
Indeed he/she may. They need a search warrant for DNA just like blood or even your fingerprints. Probable Cause is still alive (although beaten down).
A few months ago I was staying at a hotel that hosted a lot of local company's managers. Since they have had problems in the past with these managers causing problems if they are out too late, the company started up a cerfew.
To enforce this, they station a (presumably off-duty) police officer in the lobby to get the names of people who come in after a certain time of night.
The cop asked my "may I have your name?" I said "no you may not."
His jaw dropped all the way to the floor. I then told him "as long as you wear that police uniform you are under color of authority. Asking my name is a violation of the 4th and 5th amendments. You do know the Constitution, don't you?"
He was just thunderstruck as I walked away.
They will take me to prison before I surrender to random questions by the police just because they think they can.