I don't know. But you can do certainly do it in California.
Actually, you really can’t, but an explanation depends on an understanding of SC Court and, while the comment pertains to CA, my reading of the NH statute suggests that the explanation may be equally relevant to that state (‘tho I will defer to its knowledgeable citizens with personal bench experience to the contrary).
Three preliminary points: First, “informal” or “liberal” evidentiary rules in SC doesn’t mean that rules of evidence are ignored; it means that operation of SC virtually requires that rules for admission of evidence be “bent” or be flexible. Second, inadmissible evidence may be presented to the bench officer; that does not mean that it is considered in making a ruling. Third, CA does not permit attorneys in SC; NH does.
Scenario in CA SC’s: Litigant holds up a piece of paper and says “I’d like the court to see this”. Fine, it’s taken and read. It’s clearly inadmissible evidence under the Rules of Evidence for any of a dozen reasons, but the bench officer can’t spend the calendar playing advocate for one side or the other and, anyway, you can't "unring the bell". In this case, it’s an affidavit attesting to material facts, but the affiant is not there to be cross-examined by the adverse party. It would never get in a higher court over an attorney’s objection, but there is no attorney and the other litigant doesn’t know better. The bench officer thanks the litigant, moves on with the proceeding and doesn’t consider the affidavit when making a ruling. The bench officer must self-censor.
Exception: In CA, most bench officers admit accident reports prepared by law enforcement officers, because they often contain more useful factual information than even the litigants can provide (re: admissibility see Good Riddance to Bad Laws, 5 Cal. Lawyer 69 (1985) but also see Cal. Veh. Code sect. 20013 (no accident report may be used as evidence in any trial)).
Now look at NH, where attorneys are allowed and presumably can object. The quoted portion of the statute says [litigants] “should bring any witnesses they might have who can help with their case.” Assume an affidavit that says “X wasn’t liable because . . . . I saw it but have a doctor’s appointment today and can’t come to court”. If I’m the attorney for Y, I’m surely going to object, whether it’s notarized or written in blood. If Y doesn’t have an attorney but disputes the statement, am I, as the bench officer, going to give the affidavit probative value or just say “thank you"? Personally, I don’t know, but I hope that NH and no other state is so “liberal” as to give it weight, because I don’t think the Rules of Evidence mean very much in any state that will.