The DT has the same right to test anything they may think is of value.
All they do is go before the judge requesting him to let their forensic DNA expert test certain pieces of evidence themselves.
The only requirement is the state DNA expert must be present during the testing, and the DT must turnover the lab results to the state, just like the state has to turnover their lab results to the defense.
The defense rarely does that though even though they are allowed. It seems they would rather speculate to the jurors about untested evidence instead, because if they do further testing it may backfire on the defense, and the state now has the results of those tests.
Imo