Sworn statements are written or oral statements given under oath or penalty of perjury. These documents may also be referred to as sworn declarations.
While sworn statements are very similar to affidavits, they do not have to be witnessed or notarized as affidavits do. However, the person giving the statement must sign an endorsement at the end of the document, confirming that the statement is true and was given under oath or penalty of perjury.
It is up to each individual state and even court to decide if a sworn statement is acceptable in place of an affidavit.