For Confederate, Texan and similar time period notes, I find a handy first stop is
Crutch Williams' list of bogus notes. Look up the type, then the serial number. If the number on your note is listed, it's definitely bogus (the genuine example of the note with that number is usually in a museum collection); if it's not listed, then there's a reasonable chance it's genuine.
In this example, I see an Arkansas Treasury Warrant $1 listed, dated April 28 1862, numbered 128346; I think the date is a match but I can't quite read the number on yours to rule it one way or the other.
Your other option is to Google the note type and the serial number, and see if anyone else on the Internet owns one. If you find a match, it's probably bogus too - especially if yours have been sealed away in the family for years.
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...I would consider the material it is made out of to be just shy of brittle...
Replica notes are often artificially aged, to make them "look and feel old"; usually it's done by soaking them in acetic acid or other chemicals that attack the paper. My dad once brought me home a set of replica notes; they still smelled of vinegar. The chemical often creates a wrinkled, wavy effect in the paper, which I think I can see along the bottom of your note; genuine notes shouldn't wrinkle like that unless they, too, have gotten wet.
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Do all of the old money or vouchers of this nature, that's real, have printing on both sides, cause some of these don't, or is some of it one sided?
I'd have to say "it depends". Most bank and government notes should be two-sided, private scrip is often one-sided, though there are plenty of exceptions to these rules.
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Oh, by the way if these things are novelty where's that put the collect-ability?
You can go to historic sites and buy envelopes full of replica notes for a few dollars (My dad bought the aforementioned set in Richmond, Virginia). An individual replica wouldn't be worth more than a dollar, I would guess. Not too many people actually want them as a collectable item.
Hope this helps some.

Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis