If someone has been diagnosed with cervical dysplasia, should she get tested for std?

YES: The most common cause for this dysplasia is hpv, with at least have of all dysplasia caused by that virus. This is spread as an std with at least 80% of all women positive for hpv by age 50 years. Having one std, of course, means you are at risk to have attained another, so get it checked out.

Probably: Cervical dysplasia is not an std but it is almost always associated with an std (hpv). It is a good idea to be tested periodically for std's if there are any risk factors for std.