Technically, I don’t think the church has explicitly stated no further C-14 testing will be allowed on the shroud. However, I believe the RCC will never allow another test on the TS outside of the church, whether it be C-14 or any non-destructive testing.
The 1988 C-14 test has been the only test that has been authorized by the church. And as I’ve argued, the entire process of the C-14 testing was flawed. Though in some cases, the church was at fault, in the majority of cases, it was the fault of the C-14 labs and the British Museum. Not only that, the labs demonstrated improper behavior and misconduct. Their motivation was not to do unbiased science, but to further their own agenda.
Gonella accuses the laboratories of “intoxication by success” and adds: “Misconducts there
were tons. The colleagues of the 14 C behaved in a disgusting manner. Those scientists have
hatched a true plot to discredit the Shroud. At first, when they did ask us to examine a sample
of the Shroud, assured us of the utmost seriousness and completeness of the analyses, along
with the collaboration with the Custodian of the Shroud, that is the Bishop of Turin, and his
scientific advisor, i.e. the undersigned. Driven by celebrity fever, those scientists began to turn
their backs on their own commitments: no more interdisciplinary examinations, only 14 C. They
flooded even Rome with pressures so that Turin had to accept their conditions. They used the
then president of the Pontifical Academy of Sciences, professor Chagas, to get the
undersigned out of the way and go their own way”.Gonella explains: “It was blackmail. They put us up against the wall just with a blackmail.
Either we accepted the test of 14 C on the terms imposed by the laboratories, or it would break
out a campaign of accusations saying the Church fears the truth and is an enemy of science.”
https://www.shroud.com/pdfs/marinelliv.pdf
For the STURP tests, the shroud was still owned by the Savoy family, not by the RCC, so it was King Umberto II that authorized the STURP testing, not the Vatican.
Most people tend to think of the Shroud of Turin as a “Catholic” relic. While the Church does have a long history with the Shroud, many people don’t know that the Holy See only took ownership of the cloth in 1985, after the last King of Italy, Umberto II, of the House of Savoy, bequeathed it after his death in 1983.
https://www.academia.edu/51155842/The_H … d_of_Turin
The only body that would probably be able to test the shroud now is the church’s own scientific body – the Pontifical Academy of Sciences. And they release very little of their workings to the public on the shroud.
In 2002, the RCC performed a restoration of the TS. They did this without consulting any external scientific body, including any of the original STURP members.
Experts performed a top-secret restoration of the Shroud of Turin, removing centuries’ old patches and replacing a backing sewn centuries ago onto what some say was the burial cloth of Jesus, Church officials announced Saturday.The restoration was carried out with explicit Vatican permission, and aimed only to protect and document the artifact.
The project consisted of three main elements: the removal of patches and a backing sewn onto the Shroud in the 16th century; a digital scan of both sides; and photo documentation.
The restoration was done June 20 to July 23 by Shroud expert Mechthild Flury Lemberg and restorer Irene Tomedi. Vague reports of the project leaked to the media in August, enraging other Shroud experts, who argued that the work should have involved less secrecy and more international collaboration.
https://azdailysun.com/details-of-secre … 978f2.html
The 2002 restoration is evidence the church will not allow any external body to be involved with a hands on study of the shroud anymore.
https://debatingchristianity.com/forum/viewtopic.php?p=1113306#p1113306