Crimes must generally be proved "beyond a reasonable doubt", whereas civil cases are proved by lower standards of proof such as "the preponderance of the evidence" which essentially means that it was more likely than not that something occurred in a certain way. There are different standards in different circumstances. For example, in criminal cases, the burden of proving the defendant's guilt is on the prosecution, and they must establish that fact beyond a reasonable doubt. In civil cases, the plaintiff has the burden of proving his case by a preponderance of the evidence.
In American jurisprudence, impossible crime is punished as attempted crime. He can be convicted of an attempt to commit the substantive crime where the elements of attempt are satisfied.