Synopsis - The state has physical evidence in a meth lab case that has not yet been tested for fingerprints but the state has requested that the police test it to find if fingerprints are, in fact, on the evidence. The defense is determined to have the evidence tested by an independent expert and has filed a motion with the court to have an expert appointed for that testing. The problem comes in with the testing itself. Apparently, once the procedure for finding fingerprints on the evidence is completed, it would prevent anyone else from being able to do any kinds of tests on it for fingerprints.
Is there any case law out there that says who has the right to test evidence in the state's custody if there is only one shot at testing the evidence?

Article 38.35(b) give the State a general right to conduct forensic tests on evidence that it possesses.

Other than that, Youngblood v. Arizona is probably the main case on point. Basically, that case stands for the proposition that defendant's have no claim if your fingerprint testing "destroys" the relevant evidence (for lack of a better word). Youngblood is violated only if the defendant shows that the State destroyed what it knew to be exculpatory evidence in bad faith.