Is it that simple? If you are accused of a crime and the charges are dropped or a jury finds you innocent, does the fact that you were even accused show up on your criminal history?
It depends on how deep your employer wants to dig and how much he wants to pay.
For public information requests such as employment screening, typically everything will show up except your arrests. If you were tried and acquitted, it will show up, since being acquitted does not "erase" all record of your trial. It simply adds the disposition or outcome of your case.
Also, depending on the information/research service your employer uses, they may only go back 10 years. So if the employer wants your life story, he may have to pay a lot more to get it. Many employers feel that if you've been 'clean' for the previous ten years, that is good enough for them, since it is generally true that those with serious character flaws that would bring them into conflict with the law seem to get themselves into trouble more often than once in every ten years.
Arrest records are typically not public information and are for law enforcement purposes only, though there are exceptions.
In many states, it is a prohibited employment practice to inquire whether an applicant has ever been arrested, since lots of people are arrested but never even charged with a crime. Exceptions are positions related to security matters, such as law enforcement, certain banking positions, positions of high responsibility, etc.