Older relics can be tested, but the Catholic church won't really allow it, e.g. San Gennaro's blood in Naples is a flask of red clotted liquid which melts during some ceremonies, and is quite likely not blood at all. But there's a massive community of believers and thus it will not be challenged by the church.

For more modern miracles and relics the church does have a tight grip, and famously one pope threw a whole bag of Christ teeth in the Tiber river, but many older things have been "grandfathered".