Little Guy wasn't much help. They gave me the number for The Little Trailer Company, where the trailers were manufactured. Unfortunately, they are bankrupt and the voice mail box is full. Since they manufactured the trailer, I'm pretty sure they are the ones who would have to issue a Manufacturer Certificate of Origin. Little Guy was just the sales and marketing end. Found and interesting article about what Little Trailer Co. planned to do when they split with LG. Guess it didn't work out.
http://rv-pro.com/article/qa-little-trailer-co
I contacted the original owner. She's going to look through her paperwork. She originally registered the trailer in Connecticut. She said trailers are registered but not titled in Connecticut. I'm assuming they need a certificate of origin to register it in Connecticut. If she can't find paperwork she'll call Connecticut DMV and see if they have any paperwork.
So, as far as I can tell there's no title or certificate of origin ... one or the other is needed to register in Oregon or Washington. I don't think I can apply for a lost title since there never was a title issued. I'll check with DMV and see if it is possible with just a bill of sale and a vin #.
Wish I had found this out while the Little Trailer Co. was still in business.