Cryptic tuberculosis is a form of tuberculosis where the diagnosis is difficult due to the absence of typical signs like a positive tuberculin skin test or clear chest X-ray findings. In such cases, the following condition is often observed:
A negative skin tuberculin test.
A negative chest X-ray.
This combination is characteristic of cryptic tuberculosis, as the patient may have the infection, but the typical diagnostic signs are absent or subtle. Thus, the correct answer is:
\[
\boxed{C} \, \text{Negative skin tuberculin test and negative chest X-ray}
\]