Hugh Farey writes in another thread, A Report on the Bari Conference:
Bishop Marcello Sanchez Sorondo [pictured], the Chancellor of the Pontifical Academy of Sciences emailed me with these words:
The opinion of the PAS is that in order to do something scientific, another test should be carried out but since the institutions that carry out these tests are rather anticlerical, the PAS currently thinks that it would not be prudent to reopen the matter until other scientific identification systems are devised.
Although not in any sense an official statement of policy, it does suggest that at present the Vatican does indeed lack confidence in scientists’ open-mindedness, if not their expertise.
I have taken the liberty of reformatting and emphasizing part of Hugh’s comment.
Here is a Wikipedia entry for Marcelo Sánchez Sorondo.