Obviously no - there are no tests to determine the exact age of a person - especially an elite athlete in their teens known to have delayed puberty because of the intense exercising. As Dr. David Sinclair, a pathologist at Harvard Medical School puts it: "We all age at different rates at the molecular level".
It is crazy to think of this process for determining age eligibility to compete, especially when the purpose of the minimum age restrictions is to protect the athletes:
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For scientists, the best method for narrowing down a person's age is a combination of five weighted factors known as the Complex Method. It includes analysis of the pubic bones that lie just under the navel along with some vertebral bones, both sets of which start out rough in youngsters but smooth out over time; images of the femur, or thigh bone, which becomes thinner and loses bone mineral over time; dental wear; and closure of the cranium. However, it's unlikely that IOC or FIG officials will go so far as to impose these types of biological tests on the Chinese gymnasts — especially since none of these methods can definitively pinpoint any of their ages as either 14 or 16.
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They will have to rely on birth certificates, documentation, and interviews.